Uh, just my personal opinion, but draft horses were never meant to be ridden. I wouldn't get on one unless it was an emergency, just like I wouldn't try to drive an 18 wheeler to go to the store. They are just too darned heavy. Second, learn the one rein stop. Basic riding 101. Third, learn to ride a running horse. If you can ride as fast as the horse can run, then there is no reason to panic, you can plan the stopping strategy and slow the horse down when and as the opportunity arises and if it means jumping a fence then you can do that too. And if you aren't panicked the horse is less likely to keep running anyway. If they think there is a reason for the panic then they want to get away from whatever is scaring you. I have been run away with in a lot of situations over the last 64 years, including down the middle of a highway in traffic, and on 30,000 acres in the middle of Nowhere Wyoming on a huge horse with a saddle I couldn't reach the stirrups on, and yet another time when I did have to jump a barb wire fence. I have never fallen off or been hurt, knock on wood. I was scared spitless a few times and on the Wyoming one I one reined him for several miles in huge circles and got pretty tired ( I was twelve and alone), but I got the bugger stopped and we walked home, with me still on top. I am not saying this to sound smart alecky but I am always amazed at people who ride all the time, but are scared to death if the horse spooks and runs even a short distance. They fall off for no particularly good reason other than they stiffen up, lose the rhythm and boom off they go. It is different if the horse runs into something and falls himself or in the case of one friend of mine the horse ran through a barbwired fence and cut her leg almost off before falling down a bank onto a street. She and the horse survived and she didn't lose her leg but it was close. But most runaways are stoppable if you keep your wits about you and stay on. Learn to ride the fast gallop and turn safely, stop, start, etc. Learn how to ride in balance and understand what you have to do to help keep the horse from falling. Practice the one rein stop at a gallop so you don't pull the horse over. Then you will be ready when it happens again, and it will if you keep on riding long enough. That kind of practice also helps keep a horse from panicking if it finds itself running away. And of course you start out slowly and work up to actual running. Even if you think you will never need to know it, it is still an important thing to learn.