Take the fall, or hang on to the horse's face?

I have had many falls in my day. When I was young I was taught the "correct" way of falling off and thus developed a bad habit of bailing all the time, incorrectly assuming that I would be okay. I've been fairly badly injured four times in the fifteen or so years I've been riding and it wasn't until the third time that I figured out it was a smart idea to try to stick. It's been four years since I figured that out and I have only fallen off three times since then (one of which was more of an emergency dismount in which I landed on my feet, and is the only time I can ever remember landing with the reins still in my hands). Note, most of my riding career up until two or so years ago was spent in arenas or enclosed fields, and I've never had fall out in the open (knock on wood). I don't think letting go of the reins when I fall is as much of a decision as it habit. I am an incredibly empathetic person and there's nothing I hate more than accidentally yanking my horse in the mouth. If the situation warrants that I must be a little harsher than usual (i.e. My horse having a fit or trying to take off with me, which is a somewhat common occurrence) I will, especially out on the trail. But if it's an accidental situation that is cause by me, getting left behind over a jump for example, my first reaction has always been to release the reins. I will never let go of the reins while jumping, but I will let them slide through my hands to supplement an inadequate release.

During my most recent fall, which actually sent me to the hospital, if I had held on to the reins my arm likely would have been broken or dislocated in some way and some serious damage would have been done to my horse's face, as he was galloping flat out one direction and I was flying in the other. We were jumping for the first time since winter began, and long story short my trainer (who is really awesome for certain horse/rider combinations, but I will no longer be riding with her as she's not the best for my horse and me) over faced the both of us with a large oxer. I knew it was too much, but have never told a trainer no in my life, so I decided to do it anyway. Both my horse and I have the skill to jump it, but we've been through a lot in the past year and our confidence was, and still is, a little shaky. So as we approached the jump he was off balance and tried to duck out, I didn't let him as we used to have a serious refusal problem that I didn't want to revert back to, and we ended up jumping the oxer diagonally right from the base. I was thrown out of my tack but landed in a fairly balanced position (sans stirrups and reins at the buckle, which usually isn't a problem) and would have been fine if he had continued cantering forward as he generally will do in such a situation as long as we're in the arena. However, at some point during the jump the back left standard got knocked either by him or my foot, and fell into him after we had landed. He spooked, spun to the left and took off galloping like a bat out of hell, and I went flying headfirst into the ground on the right. Thanks to my helmet I ended up concussion and break free, but dealt with severely bruised ribs for a month, and am still dealing with a deep bruise to the muscle and tendon that run down the outside of my right tibia after almost two months.

Anyway, my point is that through my experience, if I'm falling inside an enclosed area I will always let go out of habit, and find it safer to do so. I'd rather spend an hour trying to catch a horse then end up with injuries to the both of us. Out on the trail is a different topic, and I think it depends entirely on the situation. But have no first hand experience as I'm lucky enough to have never taken a fall when I'm out and about. I attribute this to the fact that my horse tends to be a bit quirky and excitable when out on the trails so I tend to be paying a bit more attention to keeping my seat.

No matter what happens, my horse always stops when I fall off. Even when she used to buck me off she always stopped. My good horse, and I didn't even have to train that into her. :)

If I am falling off my horse, he has done something to cause that. I have a pretty good seat and can stay on in most situations. If I am indeed about to hit the ground, I am not terribly concerned about his mouth, and I would hang on, if possible.