> When you really need that warm hat is when you stop for any length of time.
That may be a little more than I would endorse, but I should add that our windshirts have good hoods. These can make a lot of difference - either under or over the hats.
That said, we DO take fleece ski hats in winter for sleeping. Yeah, good stuff then!
> A calico wide brimmed hat for wintertime backpacking? COME ON!
Well, all I can tell you is what we do. I could show you pics of us ski-touring with those hats on. Can get rather sunny in the snow, with lots of UV. But once again, our tops have hoods, and we carry fleece hats as well.
> Ever had hypothermia before? Even early stage, mild hypothermia?
Nope - but that is because we carry enough clothing and are extremely careful about NOT getting hypothermic. I walk and ski with my wife, and we watch each other all the time.
Well - a bit cool sometimes in the snow when putting up the tent, but that's usually a calculated gamble on what we know about each other's reserves.
Now, Heat Stress and even Heat Stroke - ah yes. I'm in Australia, remember!