All will buck you off but after being attacked by a cougar recently i think Turkoman will let you stay on horseback for the longest time possible.

I agree with you, all horses will buck you off if for example the cougar is like 2-3 meters near to your horse but i found that some horses are easier to control than others when they detect the predator and i think the andalusian is the bravest war horse in the game.

I love my turkoman