real answer is: how often do you see animals on ANY show? Unless there needs to be one, you don't see any. Too many rules about animals working on tv productions, generally not worth it.
in-universe, zombies went after that horse, so imagine they'd have eaten dogs/cats en masse as well. There'd still be a ton of them, though, and probably effective against zombies. the advantages they provide would be worth the noise for the most part. Turned out pretty useful in WWZ.
Only concern is whether the magical disease we know nothing about is transmitable to dogs, or if it's strictly human. We haven't seen any zombified animals yet. But if a dog's main weapon is his jaw, and biting caused infection, could see people actively killing dogs and cats to avoid having to also deal with zombified predators as well as actual walkers.