As a kid a friend on a farm had one particular cow who was very laid back, and would let you ride on it's back, you could even get two people on, but if you tried for a third she would buck you all off
However, I've never ridden a horse - another friend on a farm had a little sister Joanne, who had a horse called Apple, and our only experience of it was trying to catch it for Joanne to ride, I don't remember ever seeing her doing so though?.