I would guess the case could be made that any motorized vehicle doesn’t operate without a human actively making the choices about what the vehicle does, whereas a horse can take direction but will still “operate” even if the rider is blackout drunk. If you’re not on the road and not “operating” the horse, I think you could attempt to argue down to public intoxication or some other nuisance charge, especially if the horse was out of traffic and could be shown to reliably get you home without causing a disturbance. I’ll be interested to see how the courts deal with DUIs when a self-driving car is involved.