A horse can turn a person into hamburger in about a half a second, so it's wise to let the horse/rider know you are coming up behind them. If the horse seems nervous, slow down and stay out of the way. Most horses are used to everything they encounter daily, but there are a lot of variables... so if you value your body, don't sneak up on them. I think I remember that there is an actual rule in place about it. Maybe 2 meters distance, but I can't remember fore sure.
Also, with dogs, usually they are not a problem at all, but again if the horse looks nervous or overly interested (many horses think it's fun to chase dogs) you might want to hold onto them.