Unless a horse can be defined as a motor vehicle, I don't think this charge will stand. But ... and this is a very large but ... there's a reason why any attempt by a non-lawyer to interpret laws on the basis of logic, common sense, or simple morality is generally doomed to failure.
Motor vehicles are rated by horsepower, and where do we get horsepower from? Isn’t a horse the original driverless vehicle?
With a drunk in the saddle, that horse could present quite a danger to pedestrians. What if your car had eyes & felt like running over someone?
;^)