I’m not a horse expert, but I’ll wager that the horse didn’t even have the capability to understand the car was moving towards him . . . I’ll bet it looked stationary to him.
Actually that would explain the short leap too. If the car and horse were both moving toward each other at 20 mph that would be a relative speed of 40 mph. If the horse perceived the car as a stationary object, it may have overestimated his own speed going into the leap.
I think the horse was trying to prove he had the right of way.
Either that or he didn’t like the looks of the driver.