I got chased by a horse on a century -- it got spooked as a big peloton went by it's field and it jumped the fence. It split the ride - people behind it were afraid to pass it, and it was all I could do to stay ahead of it. Two guys braved the gap and caught up to me. "Ughh, ma'am, not sure if you know this, but there's a horse behind you." 
I caught up to another rider and sat behind her for a minute. As we approached a hill, the horse started gaining on us. I called out, "Horse back." Finally, it ran off into a field.
For 3 days, I get to part of a thousand other journeys.