I'm less worried about meeting mtn lion when horseback than when on foot. On horseback, and I have seen them, I roar (vocally) and charge my horse at them a few steps. Stop. And they have always left.
On foot, I frequently look back. Lion come up from behind. I also always carry a handgun for several reasons. One being in case of lion attack. Another being in case I fall off and land in some rocky, hidden draw and need help I would be able to signal.
Once, when my youngest was 8 years old, she went running up the hill in our back yard. I stood at the back door, smiling, enjoying seeing her so happy. A movement caught my eye further up the hill. She was running right toward a mtn. Lion! I had taught my children that if I yelled to go to the house or car, to do it, and I'd explain later. I yelled for her to go to the house, grabbed a baseball bat that was near the door, and went running, waving my arms and bellowing up the hill. The mountain lion, crouched lower, then turned while staying almost flat in the brush, and ran off.
If I hadn't been watching her...
Once predators lose fear of man, man becomes food.
Unarmed and on foot, we are not at the top of the food chain.