I mostly wear a helmet. When I'm riding a calm horse in a deep seat on a sandy arena...maybe not. I honestly feel more comfortable without a helmet, although 95% of my riding is wearing one.
But I've done my homework. I've read the studies. I've talked to people. I've got 3 years of riding, and have been dumped hard (without a helmet). I figure I can make a choice.
Someone new to riding? Wear a helmet. It won't hurt you, and it could save you. And I won't ride off property where I live without a helmet, because the risk is more than I want and it robs me of the fun of riding. I don't want to worry about what will happen if my horse tumbles and smack my noggin against the pavement, or against the rocks that fill the trails.
I would never, ever tell a new rider to skip a helmet. But I now do at times, and I love the feeling of riding without a helmet. It is more in tune with why I like riding horses. I know others disagree, and I don't mind their disagreeing...as long as they don't jump in my chili for not wearing a helmet sometimes, while they go off jumping 'because it is fun'.
When I go helmetless, I feel more in touch with the horse and more aware of what I'm doing. Maybe it is the risk itself. I spent years strapped in ejection seats (mostly F-4s & F-111s), and now riding is my only real risk. I'm not sure why, and I don't do it often, but I really enjoy riding without a helmet more than with.
Maybe it is related to why I jog by myself in the desert miles from help, or hike in areas without trails. 95% of the time I wear a helmet, because my mare is spooky and the raw power of a scared horse reminds one how frail the human body is. I just don't like lectures from people who take greater risks themselves...
Internet photo. Most of mine disappeared on a move from England to Texas.