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

I think different circumstances warrant different reactions.

I work in a racing yard - if you come off you better have a broke arm if you don't hold on. Can you imagine the disaster of a loose horse running back into the string of horses?? I know numerous top trainer and it is all the same - you hold on unless you are waiting on an ambulance.

My own horse I ride out on the road - you better believe my hanging off his mouth is a better option than him hanging out of a windscreen :)

A lot depends on how violently or how suddenly you get hurled off really, sometimes you just don't get a chance to stick on or hold onto the reins but given that I hate hitting the ground I will do pretty much anything to avoid it that doesnt put me at risk
I instinctively try to keep hold of the horse because if you're miles away from home its a long walk back and a loose horse galloping around is a huge risk to itself and others. I'd rather yank it in the mouth than have it run into a vehicle if I'm near a road. Horses in those situations can often panic bolt and not think about their own safety

I finally teetered on the "unhorsed" line today; I was riding without stirrups and things were going real good with posting and sitting trot, so I asked for canter; I ended up sitting too deep while trying to focus on sitting on my seatbones and she dropped to trot--- I lasted four strides of that, she was ignoring my half halt. There is indeed a line where you figure Keep Trying or Dismount, I was only unbalanced and the nut wouldn't walk so yeah, I took up my left rein and gave her a short, strong pull that evidently gave her a consequence for the screwy trot and got my butt back on the saddle. I don't like using my aids strongly -_-
But I still think if I was really out of the tack entirely I would keep a hand on the buckle and just vault off. If she were the kind of horse to bolt away, I'd let go since it was in the smaller pasture, flatwork.

My gelding and I were jumping a pretty big swedish oxer once... he got down to the base, patted the ground, and pushed off to jump over it, about 1/4 of the way over he decided he wanted to refuse instead and tried to slam on the breaks. He went down right in the middle of the oxer and I went flying over his head, reins in hand. I was gripping so hard to the reins that I tore the bridle clean off his face. I felt terrible and had to have the vet out to check his bleeding lips. Horse was fine... but I try to be a little more conscious about not ripping on my horses face when i'm about to hit the dirt.

Yup I spent many years at the track.....you hold on until the horse is running away with your dislocated arm hanging on to the end of that rope or bridle! We (and I say 'we' collectively as in the whole track community) had two nstances of a horse getting loose at the track and running all the way home through all the horses walking home.....two horses made it to the high way, one was hit by a freezer truck......so yup you better hang on!!!!

My first horse ingrained it into me to let go - because when I fell, he would bolt with me hanging onto the reins, and would kick out at me as he dragged me. If I let go, he would come to a halt a suitable distance away and watch me. He put me in hospital after nearly killing me, so some bad experiences with that one!

Admittedly he was a crazy horse, and I've tried to unlearn that instinct as I do believe hanging on is the best thing, especially with my new OTTB who would just go home... but when you've had experiences like that it's very hard to teach your reactions in that split second of 'I'm going down!' to change. I never, ever let go on the ground when leading, lunging etc, but by first reaction when I know I'm out of the saddle is to curl up and cross my arms over my neck for impact.

No offense intended, but I think it's a little too much of an accusation when you said the riders hang onto the horse's mouth. It's not intentional, if you stumble on the stairs the first reaction is to grab onto the railing. Same thing when you ride, that's the reason beginners have a hard time without the reins, they use them as balance.
I actually always blackout when I fall, the minute I know I'm getting off, my system shuts down and I wake up once I'm on the ground. I might scream, grab the reins, or do something totally stupid, but those occur when I'm blacked out and therefore if I grab the reins, it's just a reaction that I can't control because I'm not choosing to shut down, my body is.

I once asked a friend of mine who used to be a stunt rider how he organised a fall off a horse.

He gave me a complete description of how he prepared himself and the horse BUT - when I last fell off I realised that I remembered flying through the air but little else. And whereas he landed on his front, I landed on my back. He got up and walked away, I eventually managed to get to my feet.

He had planned his fall, mine just happened.

He got paid. I didn't.

But I am no stuntman.

I was actually having a similar conversation last night and someone said - there is no brave and cowardly, there is trained and untrained. People think - I will be brave if I fall off, but if they aren't trained, they won't he brave.
When something happens and I think "oh crap aim going to be in for a ride" I can stop my brain and break everything down into basic movements and moments without fear. This means usually I can keep on the horse, and if I do fall off, do so safely with the horse in hand. Because of training and experience.
For someone who is untrained and gripped with fear, its probably better to fall off without holding on.
I was trained by track people on ground handling and their mentality. You hang on unless your arm is seriously broken. Eventually after being dragged enough, you do figure out how to derail most bolts before they happen as well.
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When my horse is been a twit the last thing I want to do is go splat. So I hang on for dear life.
Not the reins, to the neck/mane/saddle.
Once she stops her hissyfit (and if I've stayed on ) I take the reins back up and turn her around and carry on as though nothing has happened.

Have seen a lot of people hauling on their pony's face/mouth though. I guess in the heat of the moment you react which ever way to save your butt

Personally, I physically cannot throw myself off a horse I just can't. I can take my feet out and let the horse get me off, but throwing myself off is just no an option I admire those who can bail out! It scares the living day lights out of me haha