True they won't mess with healthy, adult horses, but they sure will take calves, foals and people. I tell tourists and relatives "You are nothing but a kitty kibble out here."
We watch our back trail and check trees and rock outcroppings. They stalk from behind.
I had one come into our yard when one of the kids (then 8 years old) was showing me how fast she could run. We've all been stalked here.
I always carry a .38 with I'm out, whether horseback or on foot. I figure chances are better I'll need to use it to signal my location if I ever get hurt, my horse busts for home, and I can't walk out or something. But, I did use it once to scare a lion when she was stalking me and the mare I was riding started to spook pretty bad in a really rocky dry wash. I figured the sound of the shot would serve to spook the lion and scare the horse bad enough she'd race for home. I hooked my left elbow around the horn and shot once. I was right about the reaction of both. Stayed aboard the mare, but had a huge bruise on my left elbow from hanging on that hard. Lol
The general advice is to make yourself look as big as possible (wave your arms, act aggressive - or what we joke as "go banshee" on them), make lots of noise.
Those have always worked. Some backpackers carry bear spray in addition to a handgun.
They will generally avoid dogs, but some dogs hide when a lion comes around.