I never had a fear when riding or mount a horse even if I'm a really green rider
When a horse that I was riding spooked, bolted and began to canter I fell off . Or more exactly I trow myself of because I loose a stirrup when the horse bolted and I felt very insecure on him without the stirrup and with my lack of experience. I rode only green horses even if I knew that I will surely fall off at a canter or if the horse will bolt.
My other fall was when the mare I was riding changed direction while cantering. I thought that she was trotting so I forgot to slow her down so when she changed direction I fell off. I have a fear only when I think that the horse can step on me. I always remember when I fell and saw the horse's hooves so close to me. I feel that I'm unable to get myself out of his way and he will step on my arms.
But my biggest fear is not related to riding, it's related to handling horses. I think that this is because I always dealt with aggressive horses. I'm always tense and cautious around horses that I don't know and even around horses that I know. I'm in a continuous state of alert when I'm around horses because I know that they can bite me anytime. I should mention that I work with a lot of horses that bite and kick. I saw people attacked by horses, and I was kicked when I tried to catch a horse in the pasture, but it was my fault then. I tried to catch a mare that was protective with her food so she kicked me.
I worked with a horse that would attack anyone if you would approached him at a distance less than two meters. It was impossible to touch him or groom him or catch him in the pasture without being attacked. The hard part was to catch him by the halter (wile being tied) while trying to avoid his mouth and front legs and most important his hind legs.
And I think that's impossible to overcome my fears while working with dangerous horses. I am able to calm down only near 3 horses that I know that won't attack me or bite me but even with them I avoid the hind legs.