Riding any horse takes a good deal of strength if the horse is not docile. Riding a horse that has been bred to run takes a surprising amount of strength. Get that horse on a racetrack where it is focused on only one thing, and they can be darned near impossible to control. If you ever see a male jockey with only a light shirt on his upper body, you can see they are incredibly fit athletes. Most women of such small size aren’t physically able to build their upper body strength enough.