I couldn't ever "punish" my dog. Abusing your animals is something that I've never understood and I never will. It's okay to train your pets but if you'd ever kick or hit your animals, that's just unacceptable.
I've seen many horses get hit as a punishment in the stables and I can't do anything else than to feel grossed out by that. People really think it's okay to show they're superior to animals that can't really fight back. I get it that horses are way larger and they can actually harm you - but as long as a person doesn't get seriously hurt by an event that an animal causes, I really don't see it a necessary thing for a person to do. Animals have feelings too, that's what we should always remember.