Here is some guidance from the British Horse Society on how a cyclist should pass a horse.
“A horse is unlikely to see or hear you, especially if you are approaching quietly from behind,” the BHS says. “Calling out ‘hello’ for walkers or equestrians is welcome and important in alerting horses and riders that you are there.”
“Try not to get too close before you call out or you will startle both horse and rider. If possible, ask the horse rider if it is safe to pass before attempting to go by and call again if they haven’t heard you.
“If you decide to stand to the side of the path to allow equestrians to pass you, it is a good idea to make sure that the horse can still see you as it approaches, that way it will not be frightened when it suddenly spots you at the side of the track or road.
“If the horse you meet has been frightened by your presence, give the rider a chance to calm the horse and move out of your way before you move off again. Please don’t be annoyed if a horse rider doesn’t appear to acknowledge your kindness and consideration. They do appreciate your help but may be concentrating on controlling and calming their horse to avoid falling off.”