What about grabbing the bridle to stop a horse?

This is another thing you see written about a lot - somebody stepping out and grabbing the bridle to stop a rider.

It's fine when the rider is stationary.

If they are moving? I'm going to tell a story.

This happened at a small show in England. A very small show. The rings were set aside only with ropes, and the trailer area, spectator area...pretty much it was just a big field with roped off areas. In one of the rings, a rider and horse had an argument about going over a jump that ended up with the pair slamming into the jump "wing" or support and parting company.

The horse panicked and ran. It ran straight through the ring ropes and into the spectator area. At this point, somebody stepped into its path and tried to grab the bridle.

It ran straight through them. It didn't stop running until it had reached its own trailer.

They had to be medevaced and the paramedics said they were very lucky to be alive. (Not helped by the fact that the bridle had been severed by the initial accident so there was no bridle to grab, but...)

Grabbing a running horse by the bridle, with or without a rider, is something we're taught not to do - because it's highly dangerous. I've seen video of people successfully stopping a running horse, but it's not something I would attempt. When I rode in the wilderness and there was a risk of a loose horse getting onto a road, the wranglers carried lassos. In an enclosed area, we're generally taught to get out of the way and let the horse run itself out.

Doing it from another horse is a lot safer if you know what you're doing. But yes...generally, don't have your characters do this. Unless you want them to end up with a broken collarbone, several broken ribs and internal injuries - which can be fun, of course.