The problem with horses is the idiot on the horse and not the horse.
A properly schooled horse and a competent rider is no more of a problem than a pedestrian. Sadly many riders haven't a clue but have a real attitude problem and they ride horses that are not fit to be taken out of a field.
Oh, don't forget third party insurance is optional and you can be certain that the well schooled horse ridden by a competent rider will be insured and the "yummie mummy" on the out of control horse will not.
The problem, as ever, is people. Animals are mostly nice.
We ride. If the horse can't take a M3W or a Hog at 1m distance it has no place to be on the road. If you pass a horse please don't blip the throttle, don't stop, just act naturally and if the horse and rider are competent all will be well.