According to the CHP while you cannot be arrested on a DUI while navigating your horse while under the influence of drugs or alcohol, you can be arrested for public intoxication or the inability to care for yourself. If operating a moped, tractor, or golf cart while intoxicated you will fall under the perameters set to be arrested with a DUI.
Thank you Copper for your interesting questions posed to the Copper Gazette...keep 'em coming:)