When we're scouting or doing OBC events, we'll often see horses and horseback riders along the way. A couple of us are very amateur equestrians - we love horses.

While horses look calm and relaxed, they actually scare easily. Most horses don't have much experience with cyclists. In general, bikes and riders make horses nervous. Sometimes horseback riders are nervous around cyclist, too. If the horseback rider is nervous the horse will be nervous, too. A nervous horse is a dangerous horse for the horseback rider.

Here is what we ask you to do when you come upon a horse and rider:

Stop immediately; the farther away from the horse you are, the better. This helps acclimate the horse to your presence.
Turn your bike so it's facing the horse. This minimizes the visual size of the bike by partially obscuring it. This will reduce the horse's confusion about the interaction and make you and the bike less imposing.
Talk to the horseback rider. The horse will be confused by your bike; the sound of voices is common for horses, so the horse will be more likely to relax - reading you as a person rather than an unknown creature with handlebars for horns and wheels for feet.
Ask the rider what to do. Every horse has a different background. The horseback rider knows best what is wise for you to do.
Be nice to the horseback rider. In some areas of New England horseback riders and cyclists have a contentious relationship. Let's represent cycling in the most positive light possible. It's also quite possible that the horseback rider will be a bit nervous because the horse is in an unpredictable situation.
Wait for the horse and rider to go by you. Take a moment to appreciate how amazing horses are! Did you know that the horse is the inspiration for the bicycle? Without horses the bicycle may not exist. Respect.
Roll-out slowly and predictably.