Remember that a horse is a prey animal, meaning that way back they were on the menu for predators. Keeping this in mind, the bicycle is very quiet when it travels, then all of a sudden it appears behind or beside the horse...the horse of course is unnerved by this sudden appearance of the "cougar on wheels." It is instinct that kicks in at a moments notice, reactions, with out thinking, if you are in the line of fire or even close to the line of fire, you could get hurt. For your safety, I would suggest that as soon as you see the horse ahead of you and you know that you are within hearing distance of the horse and rider, let it be known that you are in the area. Once the horse hears you and the rider conversing such as "hey there" "may I get through" or "nice horse, is he ok with bikes" The rider can say "just a sec and I will find a spot where I can get off the trail" or "sure if you pass on the left I will make sure that he is ok" or...something like that. The horse recognizes the voices and human and friendly and normally the rider would turn to face the bicycle to talk and the horse can get a good look at things. If the horse seems uneasy, talk to the horse..."its ok boy, It is just me" he will no doubt settle down. The worst thing you can do is say nothing and sneak up behind the "unknowing" horse. Hope this helps