There are the three beings created of the thought of Illuvatar: Valar, Eldar, Edain. These each have a degree of freedom and autonomy within the Music.

What of beasts? Are they "of" a Vala as trees are of Yavannah? Are certain beasts attributed to certain Vala? (eagles "of" Manwe, and perhaps horses are "of" Orome? Are sea creatures necessarily "of" Ulmo?) Is their will free, and if not, to what is it subject?

Thinking about creatures like Huan (who is maybe too special for this question), Bill the Pony, and any non-person, non-Ainur creature in between, including the fox, or the fish Gollum eats. Not talking about a Maiar/Umaiar or their offspring like Ungoliant and Shelob.

I'm reminded of the Buddhist question: does a dog have Buddha nature? So, how would Tolkien go about answering the Arda version of that question?