B"H, I have humbly tried to summarize the Friedlander translation of the Rambam's Moreh Nevuchim Section III Chapter XVII (link) as regards the free will of earthly beings other than man. Hashem Yerachem if I've erred in this task. Elements in brackets, including ellipses, are my own.
The Rambam begins with views "generally accepted by our Sages" on the matter:
According to this principle man does what is in his power to do - by his nature, his choice, and his will - and his action is not due to any faculty created for the purpose. All species of irrational animals likewise move by their own free will. This is the Will of G-d; that is to say, [...] that all living beings should move freely, and that man should have power to act according to his will or choice within the limits of his capacity. Against this principle we hear, [Baruch Hashem], no opposition on the part of our nation.
The Rambam later explains his view on the matter:
My opinion on this principle of Divine Providence [...] is that in the lower or sublunary portion of the Universe, Divine Providence does not extend to the individual members of species except in mankind. It is only in this species that the incidents in the existence of the individual beings, their good and evil fortunes, are the result of justice, in accordance with the words, "For all His ways are judgment." But I agree with Aristotle as regards all other living beings and, à fortiori, as regards plants and all the rest of earthly creatures. [As regards these other living beings] action is, according to my opinion, entirely due to chance, as taught by Aristotle. [...] This is expressed in the following passage: "And makest men as the fishes of the sea, as the creeping things, that have no ruler over them. They take up all of them with the angle" (Havakkuk 1:14-15). [...] One cannot object to this theory saying, "Why should G-d select mankind as the object of His special Providence, and not other living beings?" For he who asks this question must also inquire, "Why has man alone, of all species of animals, been endowed with intellect"? [...] Understand thoroughly my theory, that I do not ascribe to G-d ignorance of anything or any kind of weakness. I hold that Divine Providence is related and closely connected with the intellect, because Providence can only proceed from an intelligent being, from a being that is itself the most perfect Intellect. Those creatures, therefore, which receive part of that intellectual influence will become subject to the action of Providence in the same proportion as they are acted upon by the Intellect.