[Mänwe]

I agree also that this is a most fascinating question, and I would add a little something that for me suggests there is another "power" that holds them. I quote from Tolkien's letters,

"...but Ents and their wives being rational creatures would find some 'earthly paradise' until the end of this world: beyond which the wisdom neither of Elves nor Ents could see. Though maybe they shared the hope of Aragorn that they were 'not bound for ever to the circles of the world and beyond them is more than memory.'...." (Letter #338) [My emphasis]

I read this and interpret it as a "something" else that holds sway over the Ents. My emphasised text, I would say, alludes to the fact that the Ents are in direct link with Arda. That they experience the same 'circles of the world', thus they are bound to its fate, and we know that the Valar created Arda in their song, themselves under the influence of Illuvatar. Consequently they have had an indirect effect upon the Ents.

Also, when Illuvatar addresses Melkor due to the discord he had been creating in the 'making', does he state that 'all' have source within him.

"And thou, Melkor, shalt see that no theme may be played that hath not its uttermost source in me, nor can any alter the music in my despite. For he that attempteth this shall prove but mine instrument in the devising of things more wonderful, which he himself hath not imagined.'" - (Silmarillion Ainulindalë)

Thus perhaps Yavanna's creation of the Ents, seemingly her own was infact just part of Illuvatar's plan. Consequently all that exists is by influence of Illuvatar and so does not have its own will.

However I am not without the need to disprove my own suggestions,

Tolkien, although his language appears to be rather colloquial (he would not make a point without meaning it, despite the apparent light hearted nature in which he writes) relative to his many other letters, nevertheless states that they are 'rational creatures'. Our very definition of the word promotes the idea of "free will". Which I think blends nicely with the quote Gothmog provided us with the conversation Manwë had with Kementari.