I have extremely thin hair and ride with my hair up. When I say thin, I mean a few mm of hair when it’s flipped up. My helmet fits the same with my hair down.
Really, the only solution for the hunter ring at an A or AA show is hair up. Tradition, ya know. It might change, hasn’t yet. With thick hair, I agree it can alter the fit of the helmet, however in my experience the biggest problem is how people put their hair up. I worked at a tack shop for 2+ years fitting helmets and constantly saw people put their hair in a ponytail, twist it and make a thick 1in+ ridge of hair, and try to put the hair tie inside too. Which meant that no helmet of any brand would fit, and they often got headaches. You need to spread it out evenly, with as much as possible outside over your ears and hair tie outside the helmet. There’s a little ‘pocket’ in the harness on Samshield, CO, etc where this lump can be without being seen. People would often go down multiple sizes in helmets when they did their hair this way, getting a better more uniform fit.
Or, you can do the jumpers.