Speaking as someone who rides motorcycles in Amish country - public roads have completely different issues from unpaved shared use trails. Someone who rides a horse on or near a public road has a responsibility to make sure the horse can tolerate the situation, IMVHO. The Amish all use blinders so the horses aren't spooked by the vehicles approaching rapidly from behind. We give them LOTS of room - slow down and keep the engines quiet - if there's oncoming traffic, stay behind the buggy until there's room to pass them - and stay alert for those little low-traction gifts the horses leave us. The same applies to bicycles. Essentially, on a public road, two-wheelers pass horses in the same way that we bicyclists expect motorized traffic to pass us.

When you're on a shared use trail, it's a whole 'nother thing. The trail may not be wide enough to give the horses much room, for one thing. For another, bicycles are the fastest traffic on the trail, and neither horse *nor* rider may be prepared for those closing speeds. Having no actual experience with this, I would be inclined to give a holler so the rider can prepare themself and their horse for the cyclist's approach well ahead of time.