Okay, so I was jumping an older schoolmaster mare yesterday, having some fun with her, but when presented with a fence with the front and back rails the same height, she stopped. Why?
Horses, compared to us, have kind of lousy depth perception and a little bit of a difficulty with object permanence. When they are faced with a fence like this:
(Image source: Craig Macubbin via Wikimedia commons)
...that back rail "jumps out" at them at the last moment, they may not even properly see it until they start to take off. Even international show jumpers will have a moment of fear at a fence like this and may stop, especially if being ridden by an unfamiliar rider.