I agree with @Software Monkey that the question's premise is flawed.
The definition in your answer is too narrow. To properly define "free will," I think we have to consider what the will is free from. Since the term, as used, is in a vacuum, we have no context, so we don't know what it is free from, without additional information.
I would suggest that a better definition would be:
The ability to choose and/or act apart from some external constraint.
If we accept this definition, then the definition you provide would be just a contextual version of this--in the context of "nature." In other words "will free from one's nature."
Likewise, we could ask the question "Do humans have free will?" and the answer may depend on context--Humans have "will free from the influence of other humans." Do humans have "will free from the influence of predestination?" I'll leave that for another question. But I hope my point is clear... The term "free will" doesn't work in a vacuum.
Now, does God have "free will?" Well, according to your definition, I would have to say no, since nothing has "will free from its own nature," apart from the possible exception of things that are able to escape this limitation by some supernatural means. And since God is the supernatural means, and there is no means greater than Him, nothing can enable Him to act apart from His nature.
I think this is like asking "Can God make a stone so large He can't move it?"