Qft. I used to mountain bike back around 1990-95. Horses on the trail would sometimes freak out at a moving bike. And the rider would look at us like it was somehow our fault that their animal was skittish.
Horse riders should be accorded right of way over any mechanized means of transport, in the same way that sailboats have right of way over powerboats.
Actually it was your fault. There are well established trail rules for meeting and passing bikes, hikers, equestrians and even motorbikes. Everyday there are thousands of meetings on the trails where there are friendly greetings and easy passages. Only takes one of the users not knowing trail etiquette to make it uncomfortable.
I trail bike, hike, & horse ride.