I'm always so nervous when I go to try out a horse to lease?

No it wouldn't annoy me! I have the same problem! I am a decent rider and I know how to take care of a horse and treat injuries, but when I get on another person's horse I freak out! I would understand because a lot of people get nervous when on an unfamiliar horse. Picture yourself on your favorite horse! Ride him like you would any familiar horse. Just be cautious about how the horse reacts to your cues. If he pins his ears when you squeeze hard, lighten up on the pressure.