I've encountered horses and riders on the street, also. I think I generally went by at my regular speed, but went around the horse wide. The riders tended to slow and/or stop the horse. I just wanted to get away from the horse as quickly as I could, as a person who generally is afraid of any animal. The riders did signal me to go on, as I tried to give direct eye contact. The only time I've encountered horses on local trails is when I've been hiking and believe me, I froze and let the horse pass.