Bombadil as a Nature Spirit
To reasonably argue that Tom Bombadil is not a Maia, we must suggest an alternative. As pointed out earlier, this requires a greater freedom to modify Middle-earth than may be appropriate for us as mere readers of Tolkien's works. However, if we could find a "unique" and simple theory that explained the known facts without being inconsistent with what we know of Middle-earth, a claim that this was Tolkien's unstated intent would probably be justified. With this goal in mind, we can begin to explore other options.
Tolkien's own comments in Letter #153 provide support for looking outside the list of "usual Silmarillion entities" to explain Bombadil:
"Also T.B. exhibits another point in his attitude to the Ring, and its failure to affect him. You must concentrate on some part, probably relatively small, of the World (Universe), whether to tell a tale, however long, or to learn anything however fundamental - and therefore much will from that 'point of view' be left out, distorted on the circumference, or seem a discordant oddity. The power of the Ring over all concerned, even the Wizards or Emissaries, is not a delusion - but it is not the whole picture, even of the then state and content of that part of the Universe."
One could read this as saying that Bombadil, despite being in nature similar to the Wizards, falls outside of the main picture because he is not affected by the Ring. However, an equally natural reading is that the picture of Middle-earth presented in LotR is incomplete in a more fundamental way. This 'active' interpretation encourages us to expand our knowledge of the "content of that part of the Universe" by identifying a new type of being, of which Bombadil is an example.
Among the first hints that Bombadil could be some sort of nature spirit is his first mention in Letters: in Letter #19, Tolkien asks his publisher "Do you think Tom Bombadil, the spirit of the (vanishing) Oxford and Berkshire countryside, could be made into the hero of a story?" Like the early drafts of LotR, this 1937 letter cannot be considered trustworthy: Bombadil may have changed a great deal as he was assimilated into the legendarium. However, it provides a starting point for our investigation, showing that Tom Bombadil was a "nature spirit" when Tolkien first imagined him. It seems reasonable to wonder if this view remained unchanged.
Canonical support for this claim can be found in Galdor's statement at the Council of Elrond: "Power to defy our Enemy is not in him, unless such power is in the earth itself. And yet we see that Sauron can torture and destroy the very hills." Galdor directly associates the power of Bombadil with that of "the earth itself", and even uses Sauron's ability to destroy the hills as an argument that Sauron could defeat Bombadil. This may be the strongest evidence that Tom is essentially related to the natural world. It is also difficult to reconcile with the Bombadil-as-Maia theory: a Maia may have helped to shape the earth, but the ability of another Maia to reshape it elsewhere is hardly an argument about their relative power.
Goldberry as a Nature Spirit
Because Bombadil is said to be "Eldest" and otherwise unique, he is a poor starting place for understanding a general class of beings. On the other hand, Goldberry is a relatively simple character, so we begin with her. The evidence suggesting that she is a nature spirit can teach us about them as a class, and because she and Tom are likely similar in nature this gives indirect evidence about him as well.
One of the strongest statements supporting this identity for Goldberry comes from Letter #210, in which Tolkien says "We are not in 'fairy-land', but in real river-lands in autumn. Goldberry represents the actual seasonal changes in such lands." This letter, written well after LotR, indicates that Tolkien saw Goldberry as a nature spirit in some sense, one associated with river-lands and seasons.
The repeated statement that Goldberry was "daughter of the River" also fits well with this idea. If nature spirits in Middle-earth arise in association with features of the natural landscape (a possibility discussed below), it would be fitting for a spirit connected to the Withywindle to be called its "daughter". Names aside, Goldberry's voice is repeatedly compared to water and the river, and her songs evoke potent water imagery:
"Then another clear voice, as young and as ancient as Spring, like the song of a glad water flowing down into the night from a bright morning in the hills, came falling like silver to meet them".
--"The Old Forest"
"...there came falling gently as if it was flowing down the rain out of the sky, the clear voice of Goldberry singing up above them. They could hear few words, but it seemed plain to them that the song was a rain song, as sweet as showers on dry hills, that told the tale of a river from the spring in the highlands to the Sea far below."
"Goldberry sang many songs for them, songs that began merrily in the hills and fell softly down into silence; and in the silences they saw in their minds pools and waters wider than any they had known, and looking into them they saw the sky below them and the stars like jewels in the depths."
--"In the House of Tom Bombadil"
"...but at that moment a clear call came rippling down."
--"Fog on the Barrow-Downs"
None of this means that Goldberry must be a river spirit, but it certainly fits that idea very well. The imagery is frequent and unambiguous: Goldberry certainly felt closely tied to the river, whether by nature or by choice.
A close connection with the Withywindle is also indicated by Tom's story of finding Goldberry: in the chapter "In the House of Tom Bombadil", Tom sings of water lilies
"in a wide pool, deep and clear, far down the Withywindle; there they open first in spring and there they linger latest. By that pool long ago I found the River-daughter, fair young Goldberry sitting in the rushes."
Anyone can sit in the rushes by a river; this does not mean she was a nature spirit. However, like the earlier quotes this is consistent with the notion that Goldberry was intrinsically associated with the Withywindle and its seasons; it may be significant that Goldberry's pool held the most lasting spring and summer lilies.
A seasonal connection is also found in Frodo's verse at their first meeting ("In the House of Tom Bombadil"): "O spring-time and summer-time, and spring again after!" Frodo connects Goldberry with spring and summer, although we don't know the inspiration for his words: one of Bombadil's unrecorded songs, some deep perception of her true nature, or simple poetry. The first quote describing Goldberry's voice mentions spring as well.
A last and very subjective argument along these lines comes from Frodo's reaction to Goldberry's voice at the beginning of the chapter "In the House of Tom Bombadil":
"He stood as he had at times stood enchanted by fair elven-voices; but the spell that was now laid upon him was different: less keen and lofty was the delight, but deeper and nearer to mortal heart; marvelous and yet not strange."
This reaction seems very appropriate in response to a nature spirit associated with the seasons. Where the Elves feel strange to mortals because their immortality holds them above the world's changes, a spirit of the seasons might seem marvelous but would be familiar to them on a very deep level: change is a fundamental aspect of mortal life. This quote also gives another hint that Goldberry is not one of the Ainur: the Ainur always seem even more "lofty" than the Elves.
Other Possible Nature Spirits
If Bombadil and Goldberry are nature spirits, it is possible that they are the only ones Tolkien ever mentioned. However, the more potential nature spirits we identify, the more likely it is that such beings were part of Tolkien's vision for Middle-earth. Also, several examples would be necessary to learn anything about them as a general class. While the examples that follow are not meant as convincing evidence that the "canonical" Middle-earth contains nature spirits, they support that idea and help inspire the specific theory about them presented in the next section.
Tolkien's earliest stories explicitly contain "nature spirits" of a sort. "The Coming of the Valar" is The Book of Lost Tales I tells of "the sylphs of the airs and of the winds", "the spirits of the foam and the surf of the ocean", and
"the sprites of trees and woods, of dale and forest and mountain-side, or those that sing amid the grass at morning and chant among the standing corn at eve. These are... brownies, fays, pixies, leprawns, and what else are they not called, for their number is very great... they were born before the world and are older than its oldest, and are not of it, but laugh at it much, for had they not somewhat to do with its making, so that it is for the most part a play for them..."
In the language of the later stories, these spirits were the Maiar. However, while the "Valaquenta" says that "in Middle-earth the Maiar have seldom appeared in form visible to Elves and Men", these spirits seem to have been known throughout the world.
Later revisions hint that Tolkien changed his mind on the origin of some of these spirits. The last outline for "Gilfanon's Tale" says of the "Shadow Folk" that
"These were fays (C); no one knows whence they came: they are not of the Valar nor of Melko, but it is thought that they came from the outer void and primeval dark when the world was first fashioned."
("(C)" refers to an intermediate outline; I am not sure what it means here.) In the Lost Tales, all of the Ainur who entered the world were called Valar, so at least some "fays" now had very different origins. While none of this reflects Tolkien's later vision, it shows that he did once imagine nature spirits in Middle-earth.
As already stated, there are no obvious examples of nature spirits in Tolkien's later writings, and most of the beings in Middle-earth are explained in one place or another. However, there is at least one wholly unexplained race in the canonical texts: the giants seen by Bilbo in The Hobbit. While we cannot prove that they are nature spirits, that possibility suggests some interesting conclusions.
Some have suggested that the giants were not real, but this claim is difficult to support. Bilbo both sees them ("he saw that across the valley the stone-giants were out, and were hurling rocks") and hears them ("They could hear the giants guffawing and shouting"). Thorin worries about being "picked up by some giant" and Gandalf "was far from happy about the giants himself." Gandalf mentions them later, too: he hopes to "find a more or less decent giant" to block the goblins' new gate, and he tells Beorn about them. In short, giants have a firm presence in The Hobbit, and it is not our place to reject them. They may even be present in LotR: some suggest that the stones that fall near the Fellowship on the Redhorn Pass were thrown by giants, though they remained unseen in the blizzard.
What are giants, and why are they absent from Tolkien's other published writings? (They did appear in drafts of LotR, but most references to them were either removed or evolved into the Ents.) They could be very large humans, just as hobbits are very small ones, but this does not explain their lack of involvement in Middle-earth. They could be independent Maiar with a fondness for chaos, but this also leaves a great many questions unanswered. They could be a particularly large breed of troll, unable to travel far from their great mountain lairs lest they turn to stone in the sunlight. Many explanations are possible, and none are entirely satisfying.
We are interested in the possibility that giants are nature spirits, so we will look for similarities between them and Goldberry with this possibility in mind. The more similarities that we find, the more likely it is that they are "related", and the better our understanding of nature spirits in general.
One clear similarity between Goldberry and the giants is that both seem to stay in a relatively small area. Goldberry is only seen near the Withywindle, and giants are only seen high in the mountains. Another is their affinity for particular aspects of their home territory: as noted above, Goldberry is closely connected with the Withywindle, while the giants are called "stone-giants" and seem to spend a great deal of time with rocks. This suggests a general rule: nature spirits are associated with some particular feature of the landscape, and are unable or unwilling to be separated from it. Just as Goldberry is "daughter of the River", each giant might be the "son" of a particular mountain peak.
A more subtle similarity is that they are all connected in some way to the conditions of the world around them. We have already seen evidence that Goldberry is associated with the growing seasons, from Tolkien's direct comments to Frodo's verse to the spring and summer lilies of the pond where Bombadil found her. For their part, the giants are only seen during the great thunderstorm, and if they do appear in LotR it is in the midst of a blizzard: their connection appears to be with violent weather.