Just like Ram said - animals' skin and coat need to "breath" and be able to sweat.
I have seen both cats and dogs wearing clothing. Personally, I think it's stupid when people dress their animals frequently just for the cuteness factor.
Now, for those animals, like Melody mentioned, who have no real fur to keep warm in the cold winters, then putting on a jacket and boots for bathroom walks outside is one thing. But when the animals come inside, take the clothes OFF! LOL.
I also don't mind the Halloween costume, but only if they are wearing it for an hour or so as we then go back to the sweating and such subject.