I'd buy her a helmet for her birthday, to serve as a not-so-subtle clue about her head safety--yet remaining civil and kind about it. If nothing else, at least she'll know you care enough about her riding habits to say something!
As much as I believe that her decision not to wear a helmet is dangerous and downright stupid, in the end, if she decides not to protect herself while riding, that is her choice, and there's not much you can do as her friend to change her mind. That being said, if they are riding on a stable property, the barn owner REALLY needs to implement a helmet requirement to circumvent riders like this - if not to protect those riding on property, to protect her own farm in the event of a fall (insurance, liability, lawsuit, etc).
I work with individuals with disabilities. Some were born with their disabilities. Others have brain injuries. There is a fine line between providing services and needing services.
Tell her you won't ride with her unless she has a helmet on. I actually used to ride without a helmet, and my friend told me that she wouldn't go with me unless I wore one. As a long time endurance rider, she said she had seen too many accidents--she wouldn't let friends take risks.
Let her know that she is going to look and feel way less stupid in a helmet than what she will if someone ever has to wipe her butt for her and change her everyday. That sounds crude, and I know that a catastrophic injury like that can seem unlikely, but why on earth would any intelligent person take the risk? It's just a helmet and it's been proven over and over again to have saved lives and to have prevented horrific brain injuries. You never know when something unexpected will happen. Show her videos of the famous dressage rider, Courtney King Dye, a 2008 U.S. Olympic Dressage team member, who suffered at terrible head injury from a fall during training, who is still undergoing therapy and may never be the same. It can happen to anyone, on any horse, at any time.
I know that before I was ready to wear a helmet no one could have pushed me into wearing one. Do you wear a safety vest? (I do not right now) Imagine if a friend tried to push and guilt you into always wearing a safety vest because they believed it was unsafe to ride without one. For now I believe the best thing you can do is wear yours by example and quietly lead the way. The more you pressure her the more she may push back and resist wearing a helmet.
I know that before I was ready to wear a helmet no one could have pushed me into wearing one. Do you wear a safety vest? (I do not right now) Imagine if a friend tried to push and guilt you into always wearing a safety vest because they believed it was unsafe to ride without one. For now I believe the best thing you can do is wear yours by example and quietly lead the way. The more you pressure her the more she may push back and resist wearing a helmet.
I've noticed that helmet use is a very cultural thing, and it sounds like your friend comes from a background where helmets just weren't a part of riding. It's hard to override someone's lifelong perception, and to be honest, you will probably never change her mind completely. It sounds like your heart is in the right place. You're not trying to "win" this; you truly want your friend to be safe. So maybe on a day when she's about to jump or school a greenie, say, "Could you wear a helmet while you're doing this? I know it's silly, but do it for me?" If you're sincere and only bring the issue up on those specific occasions, she'll humor you. And who knows? Once she's used to wearing one sometimes, maybe she'll be more apt to use it for everyday rides.
All you SHOULD do is encourage once or twice and then let it go. Your friend's choice of risk management is HER choice; not yours. You don't have to agree with it, but you should respect it, just as you would expect her to respect the choices you make.