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.
Viggo Mortensen bonded so much with Uraeus (Brego in the film), the horse he rode in the Lord of the Rings series that after they finished filming, he purchased the horse from its owner. He also bought his stunt double's horse for stunt double!