+1. I'm surprised this hasn't been done yet! I can't think of anything taggable as hat that isn't worn on the head (and headwear has ~4000 posts), so this seems like a go-ahead implication.

I will say, however, that I don't know what the intended distinction is between the headwear and headgear tags. The other tags suggested to imply headwear seem fine to me as well, with the exception of mask: for example, the mask in post #1500429 seems closer to eyewear for me.