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 :)