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.