I've run across a website out of Montana, that is a carriage driving school. That's the only one I've seen, although I haven't been looking specifically for the driving school. If you're in OH, there must be Amish or Menonite communities within reasonable driving distance. Maybe someone in those communities would be willing to teach you to drive for a reasonable rate. That's where I would turn first. Good luck.
Looking at the trail through the ears of my horse...wonderful!