It's so annoying when people I don't even know ask me this. If you get to ride my horse, I have got to trust you a lot to let you have the reins of something that important to me. it's like riding someone's car without them in it.
the Doctor has two hearts. many horse people have expressed riding as being the art of becoming two hearts moving as one body. maybe the horsey Whovians find themselves the most like the Doctor when we ride.