At the following URL you can see the reactions of two cats briefly in freefall. Not surprisingly the animals cannot instantly work out how to react to a totally alien environment.

Without hard evidence, I suspect that, given a few minutes, hours, or days under suitable circumstances, they would adjust pretty well.

However, I am not inclined to try the experiment.

http://nerdapproved.com/misc-weirdness/cats-dont-belong-in-space-video/