While I've not been around horses much at all, even I know that horses can spook. You don't encounter many horses here (very urban), except for perhaps a police horse in training, or an event that is likely to have mounted police present...and that's a different sort of animal.
On the MUP I ride on at home, horses are allowed. I've only ever encountered one once. The rider was very polite and let us go by. Trail rules say that you need to yield to horses--and I get that. What these people don't seem to get is that--and this goes for any animal--it's their responsibility to know how it reacts to stress and to control it accordingly, including avoiding those kind of situations as much as possible.