I started riding (after 20 years off) at the beginning of 2011. I was terrified of falling off. I have a very safe mare, but some days I couldn't even get on her because I was too scared.
What helped is developing a really good seat. When I did ride, I'd spend the last ten minutes of a ride (when the horse was nice and calm, and no spooky things going on) riding without stirrups, and doing exercises to help me feel what correct balance is. Like, holding your arms straight out from your sides and then twist your upper body without moving your hips or seat; or raise your arms over your head while allowing your hips to continue following the horses movements.
In dressage, it's no big deal to have your trainer put you on a lunge line so that you can focus on developing a more solid seat. The better your seat, the more secure you feel.. and the less fear you'll feel.
Developing your seat also allows your hands and legs to work independently of your body. So even if the horse is moving out, you can follow the movement while maintaining control of the horse.
I would suggest doing pilates, or any kind of stretching/strengthening exercises that make your core stronger. The stronger your core, the better able you will be to stay balanced, the more balanced you are, the less you'll feel like you could fall.
Also, there are numerous video's and articles on exercises you can do mounted that will help increase your awareness of your seat, and develop a more solid seat.