Medieval hats are something that we mostly know from images - the finds are, unfortunately, very rare. At least that is to my knowledge... should you have a treasure trove of medieval hats somewhere, let me know!
So I was very delighted to hear about the find of a medieval hat that is in the Västerbottom Museum in Sweden. And there's even information about it online, you can find it here. The images directly in the web entry are not too good, but there's a colour photo in the pdf that can be downloaded on the site. I'm a little sad that the dating is only "medieval", which is not very precise... but I'll take a non-precisely dated hat over no hat anytime!