Is Tom a part of the natural world, meaning sprung of the incarnate world that Melkor marred? I've never thought so. That the Ring has no power or hold on him at all suggests that he comes of untainted roots, sent to or placed in Middle-earth with some other purpose to which he is so singularly dedicated, anything else is of little or at best temporary importance to him.
It's because of this (and his claim to be "oldest and fatherless," not to mention his query, "Who are you, yourself, alone, and nameless?") that I believe he's an Ainu. As I have studied Tolkien's works over the years, I've wondered if what he is is a Maia of Yavanna, sent to ME long ago, perhaps to check up on things for her, and/or to remain there as a guardian, before the awakening of the Eruhini. What tends to support this possibility (at least in my pointed little head
) is an examination of the few Maiar we know, especially those who are specifically sent as messengers or emissaries of those they serve. Both Sauron and Curumo were once Maiar of Aule, and both of them demonstrated reflections of Aule's desire for order (what do you call it when a person keeps rebuilding things that another tries to destroy?), as well as his impatience (as in his fashioning of the Dwarves). Unfortunately, they didn't pick up on Aule's willingness to serve humbly. Eonwe and Olorin are both Maiar of Manwe, and they both demonstrate his qualities of leadership, as well as his naievte in regard to evil (all three of them allowed freedom to people who had already amply demonstrated that they could not be trusted and would, in fact, turn on anyone, including their own kin, a freedom that invariably led to bad results).
So when I consider Yavanna's servant, Aiwendil, and what became of him... it looks not unlike the situation of Tom. Aiwendil became so enamored of the kelvar and olvar of ME, he forgot about his greater mission, spent more and more time around his home in Rhosgobel, and in the end did not return to Valinor (as Tolkien tells us in his poem fragment, "Wilt thou learn the lore/of five who came from a far country?/Only one returned..."). Tom is remarkably similar. He loves the land that is his domain, and all that is in it, and he does have knowledge of the world beyond it, but he will not leave it. It seems rather unlikely that the Old Forest is a place of such incredible importance that it truly requires a powerful guardian -- at least now. Perhaps once, it did, or perhaps once, Tom had a mission and a purpose that extended well beyond it. Orome and Yavanna did indeed appear to be the two Valar who showed the most interest in ME before the awakening of the Elves, and they also seem to be the ones who did the most active searching for them. If Orome himself would go to ME, hunting the monsters of Melkor and searching for signs of the Children, might not Yavanna have sent her own servants on a similar mission? Tom, I think, was one of them who became like Aiwendil: he so loved the world he had been sent to help, he put down roots of his own, and now will not leave the place he has made for himself.
If I were to try to compare Goldberry to any Maia we know, it might well be Uinen, for, aside from her appellation as the "River-daughter," she seems to be a calming influence on Tom, much as Uinen is to Osse, a gentler, more accessible -- more "normal," if you will -- presence that tones down what might be seen as his excesses.
Well, it's just theory, but most of it has been bouncing about in my brain for some years. Just another two cents.