I may be misinformed, but i gather that the law takes the sort of view to Horses and Riders that we would like it to take towards cyclists, that is it generally comes down on their side. There are various possibilities as to why, that horses have been around a lot longer than cars and so the expectation has always been that cars should accommodate horses rather than vice versa. Also that judges historically have tended to be a bit posh and therefore riders themselves. Although bikes predate cars by a bit, and there was an early upper class craze for cycling, cycling didn't penetrate upperclass culture to the extent horse riding which was, and is, deeply embedded.
Horse riding friends do say that for all that's worth, they do suffer the same crap and inconsiderate to downright dangerous and vindictive driving as cyclists do. Selfish cockwombles do seem to at least not be discriminatory!