The national Swedish dressage commity has decided that from 2017 and onwards you are only allowed to wear an approved helmet while doing dressage competitions. It will no longer be allowed to use hats.
As a pro cap person I truly believe this is one of the steps forward to make horse riding more secure. Accidents can happen to the best of us, just like Morgan Barbancon when her horse got scared and she got dragged head first over the pavement as her horse ran away. Pretty sure you would wish you had a cap on if that happened to you.