I come across horses in the woods when I mt bike sometimes or if I'm in a state forest. Each horse will be different. If in close quarters like the woods, when I do come across one coming in the opposite direction I come to a complete stop no questions asked. I sit on my bike and wait until the rider lets me know that either this horse is ok with it or not. I yell out and make the rider tell me. I don't want to be guessing what the facial expression of the rider might be at distance or guess what the horse might do. If come up behind them suddenly I slow down and call out to them with enough distance in between warning them there is a bike rider behind them and if it is ok to pass. Same if out on pavement. I've done this and a few times and they yell back saying the horse is skittish so I let them stop the horse and prepare, then I slowly ride by without any sudden moves. I've ridden a lot and I've been on horses that freak when a silly little plastic bag or tumbleweed grass blows by and on some riding near roads where big roaring motorcycles go by and they aren't fazed a bit.