Hold on and try not to fall off when the horse bolts? LOL
And trust me, you won't see he cougar before it sees you.
Cougars, being a predator, will be a natural threat to the horses. Your horse will feel threatened and either freeze and run like hell the other direction which will cue a predatory reaction from the cougar.
If you are in well-known Lion country, ride in a group and avoid th ehours of dusk and dawn, which is prime Lion hunting times. And for th elove of god, listen to your horse. He's going to see something before you do. Watch his body language. Snorting, suddenly stopping, ears forward, wide eyes.....All signs that the horse sees something. But if you do see a lion, do your best to keep the horse calm and slowly, very slowly, move away. DO NOT RUN! I cannot emphasize this enough. And no disounting unless its absolutely necessary and keep a knife or pepper spray in your saddle bag or fanny pack. If you get thrown from your hrose, get up as fast as you possibly can and don't worry about the horse. He'll get away just fine because the Lion is going to see you as easier prey. Get up and make yourself look big, puff up, wave a jacket, keep eye contact at all times. DO NOT ADVANCE THE LION. If you move toward him he will take it as a challenge and want to fight back. Be defensive, not aggressive.
And I know I've said it twice, But NEVER RUN! You ever seen that tape of cheetahs who were hunting the gazelle, and when the two male gazelle's were fighting they didn't attack because the gazellesweren't running. Running triggers an instinct for the cat to chase and kill. And also, don't play dead. Cats aren't like bears. You play dead and you will be dead.
Pssh.I didn't pick up the wrong lead
It's called a counter canter...
...A very advanced maneuver.