Does drunk horse-riding merit a DUI?

The story: Two men from Austin, Texas, were arrested after riding a mule and horse through the city's East Sixth Street district. The two men were initially charged with drunken driving, but the charges were reduced to public intoxication as the four-legged creatures could not be considered "motor vehicles." Only in Texas? Apparently not. A Montana public service announcement (see video below) advises drinkers to ride a horse home after a night out to avoid getting in trouble. Should riding horses while intoxicated merit a DUI?
The reaction: Some states hold that a horse is a vehicle, says Stephen M. Bainbridge at his Professor Bainbridge blog. North Carolina and Kansas agree that the word vehicle is broad enough to cover "not only automobiles and animal-drawn vehicles, but every device upon or by which any person may be transported," including "ridden animals." But Utah, for example, says that a horse is not a "device," whereas a vehicle is. That's right, says Texas attorney David Escamilla, as quoted in the Austin American-Statesman. "To be absolutely sure, I watched a few episodes of 'The Lone Ranger,' and not once did I hear the masked man refer to Silver as a 'device.'" See the ad: