In my experience it's best to dismount and allow the horses and riders to move on until we are out of view. Something about a bicycle spooks horses.

This might also be a food discussion for the Facebook group. Also ask your friend what is the best strategy for being chased by a horse with no rider?

My wife who is a horse person said the best thing for bicyclist to do is let the horse rider know that you are there about 4-5 car lengths ahead and move to the other side of the lane.
Bill