Well,... I got nine horses,... and ride most of them. I "ain't " no cowboy,... I'm a horseman. Don't got no cows,... don't want no cows. I rope and cut a wee bit with friends. I see a lot of "concrete cowboys" who have never tacked up a horse and have no idea which side to mount. But they sure got some nice hats,... and them "Puerto-Rican fence climbers" ( fancy-dancy western boots with the big heal and sharp toes) are just the cats arse.
On hats,... the brim is paramount. That is what you form and make the hat functional. I have a "Montana". I need a lot of shade and with this hat,... I can sell shade. Hat band? Not really. I have a "stampede strap" that is braided rawhide and that does give some decoration to the brim. It comes up each side just in front of the ear and circles the crown. The hat is 100% beaver and you can wear it in any weather,.. rain, shine, snow,.. it stand up to anything.
I do have a "dress hat" with a gold braided hatband. I wear that to weddings, and funerals and such. Looks nice, but useless in the saddle....