The only kind of hat I like to wear is a boonie hat. In case you're not sure what a boonie hat is, here's a picture of me wearing one.
Anyway, I haven't been wearing it much since I cut my hair short, but I'll wear that hat usually when it's long, especially while I'm playing footbag cuz my hair can get in the way, and I like to stall it on the brim sometimes. I still don't think I'd consider a hat footbag equipment. I guess that depends on the person, whether or not he/she wears a hat, and whether or not he/she uses the hat as some kind of aid in playing footbag.
By the way, goodieshoes, I like the mask.