Hang on. If the horse gets a tug on the mouth, so be it. He shouldn't have let you fall off in the first place! :) LOL
Seriously, though, I agree that in an arena you have a choice: do what works for you and your horse; Exception: if jumping I would advise letting go.
If not in an enclosed area, hang on. Exception -- eventing; but those people are nuts anyway
(right MIE?) and there is a support system on site for the riders and horses.