When I used to show, I wore my hair long. I'd do a single braid at the back and then double it up and stuff it in the hunt cap. I had to buy a slightly bigger one to do this. If your hair is shorter and won't take a braid, perhaps use a hair net.
A hunt cap, by the way, is not unlike a riding helmet in look and usually is covered in a velvet like material typically in black, dark blue and sometimes brown. While it's rigid construction (and that in itself would provide a little protection), it's just not as 'bulky' because it doesn't have the protective insultation.
Yes, Hunt Caps are still legal for riders over 18. Youth riders can not use hunt caps, at least in NASMA they can't. Not sure about AQHA.
I would put your hair into a braided bun, maybe use a small hair net that Dressage people typically use that is nice and showy, and covers the bun. I showed in the A circuit in NASMA, and that's all I did. Enjoy! :)
Pardon me for asking, but what is the purpose of one? I'm not at all trying to discourage you from using one, but from the pictures it looks almost exactly like a normal velvet covered helmet except without the added safety benefit. Why not have a slight amount of bulk so that you have essentially the same appearance plus the extra safety?
In AQHA, hunt caps are legal for youth. It's actually uncommon to see someone not using one.
Part of the reason that I bought one is because I compete in english showmanship for my equestrian team, and a hunt cap just looks a lot neater in showmanship. I decided to use it for my flat classes as well because IMO it does look better and I want to give myself every little edge that I can. If I ever felt unsafe at a show though, I would switch over to a helmet without a second thought.