I doubt the cat is declawed (or at least not the back claws) as vets will not usually declaw the back claws and they were the ones sliding. I am not a fan of declawing cats myself. That said, a cat's back claws are vital to a lot of things cats do and are not usually a cause of any problems.
No, I'm sure it wasn't declawed, especially the hind feet. But I don't remember my cat (Granted, it was 45 years ago) ever having problems walking on ice, and we lived on a lake.
