This morning we made the mistake of running past a couple of horses coming from the opposite direction on the towpath. Typically, I try to walk, or shuffle, but today, while in the middle of a workout, I proceeded ahead. The riders didn't think much of it, but the horse evidently did and, in turn, tossed said rider. The rider was okay, but it was a scary and tense moment nonetheless.
So, the moral of the story - walk, do not run, past horses.