Not quite the ordinary ones. There is a Pokemon by the name of Ponyta that starts off as a pony, but can evolve into a horse. But there are a large variety of Pokemon you could choose to ride if that is not to your liking.

I have some spare Ponyta eggs if you find yourself ever in need of one, although you might find another Pokemon you might choose to ride through the Breeding Centre instead. Well, once your hands are not full as is.