If you're on someone's private property, and they might be liable if you're hurt, I would think they have the right to request helmet wearing.
Whether that would hurt their business, I don't know. I think it's kind of like seat belts, once you get used to them they become a habit. We don't even think twice about football players having helmets.
I would think helmets themselves could cause some damage also, when one skiier plows into another. Football players are carefully trained to use their bodies and heads, so to speak, to not harm other players.
I've been the recipient of some very large bruises due to out-of-control skiiers, but a helmet wouldn't have helped me take a blow to the side of my body.
There are lots, I'm sure thousands, of ski accidents every year, usually broken limbs; no way to prevent them all. Orthopedic docs do seem more available in those areas. The idea that swishing down a snowy or icy mountain slope, with dozens of other skiers and big trees all around, is not risky, would be a delusion.