If the fall is "slow", I hang onto the reins because I'd rather not chase a horse down. If I'm pitched at a high speed, I let go. Mainly because I don't care what or where the horse is going. I'm focused on myself.
Its all in whats on someone's general instinct list. Self preservation is different for everyone. If someone's instinct is to hang on, they're going to hang on. If someone's instinct is to let go, they'll let go.
My personal preference is to let go, simply because I don't want to be whipped around into an awkward landing position or dragged. I want to be clear of the 1000lb animal that's acting irrationately enough to get me off. I'll catch the horse when I get up or if I'm in No Man's Land and left for dead, I'll use a cell phone or smoke signals to get home.
But really, at a high speed dangerous fall, no one is thinking about their horse's mouth. They're thinking about their immortal soul and how to save their own skin. If their reaction is to keep gripping onto whatever landline they have left, they'll hang onto the reins. My own instinct is to let go and save myself.
I knew a guy who would never let go. One time I saw a horse flip him over its shoulder and take off, and the horse galloped off into thd sunset with my friend hanging stubbornly onto the reins, swearing until they were out of sight.
And those who were seen dancing were thought to be insane by those who could not hear the music