Yes, I thought that was a pretty good definition of “free will”.
The libertarian version of free will insists on that. It insists that “we could have chosen differently”.
The compatibilist version of free will is silent on whether our choice affects the future. It is compatible with determinism, and determinism would rule out affecting the future. But compatibilism doesn’t require determinism, and we could be in a world where choices do affect the future. So I suppose that becomes a question for cosmologists, though not a question that they could actually settle.