Almost impossible, really.
At least with our horse system and another horse system I'm aware of.
Our horses actually change the phenotype of the rider to appear mounted on a horse. When mounted, the horse and rider are a single object. If attacked, the combination uses the rider's AC, the rider's HPs and so forth. In other words, you're not riding a horse, you're running around looking like you're on a horse, from a mechanical standpoint. Only when dismounted are the horse and rider actually two separate creatures.
Hitching a ride would require somehow having another set of phenotypes for dual-ridership, some way to completely disable the passenger during the ride and so forth. Quite honestly, we have enough problems with the current system. Adding another layer of complexity on top of it would be ugly.