I live in New Orleans and the police on Bourbon St. ride specially-trained, very large horses for crowd control. I’ve definitely seen some drunk tourists try to resist an officer’s command to calm down by trying to push back on the horse and the horse just being totally unphased.
I had to move a horse, to fill its water bucket while it was eating. I tap and talk, nothing. I push, can't. I had to punch it literally as hard as I could so it would acknowledge me. They have really thick skin.
Disclaimer: Don't punch a horse if you don't know it and what you are doing. They get scared easily and you won't be the first to get your jaw wired back together.