I'm pretty sure it depends on the state and whether or not that state considers a horse to be a vehicle/device. Alabama, for example, I believe does not consider a horse to be either, while I think California does. There's this story that sometimes gets submitted to TIL-type communities where a man from Louisiana was decided to be ineligible for a DUI charge after doing exactly that, but he was still given a court summons for "disturbing the peace by intoxication".