Daughter used to be a gymnast and i think she'd have caused herself and the rest of her team and her coaches, more injuries wearing a hat than not wearing one in the gym!! Guess the risks have to be weighed up. The horses are very carefully chosen for their temperament and steady way of going and they are always on the lunge. It is just like gymnastics on horse and if gymnasts can swing round the A bars or sommersault on a beam then i am sure they can vault on a horse without protective headgear on!
can you imagine trying to do serious vaulting with a hat on? it would so unbalance you! It's no greater height to fall from than when doing normal gymnastics and they dont wear any protective gear.