Quote Originally Posted by gRomoZeka
Great! Thank you, brandonp. So "headwear" will do.
By the way, "head covering" is a direct equivalent of Russian "головной убор" (I was not aware of its existence). But I googled it, and it seems that it's used mostly when talking about religious headwear. Is that true?
Yes, that's why I didn't suggest it in the beginning. Perhaps someone with very little religious exposure would not make that connection, but I believe most people would.

Also, for your example, 'headgear' would also sound good. In fact, that was the first word that came to my mind when I pictured doing what you described. 'Headwear' is good too, but I'm not sure I would call a helmet 'headwear'. For your example, though, I don't believe it would matter either way. I don't expect the dork wearing the helmet would object. He's probably just happy to be with people.