I buy my hats here. Everything is custom made, not cheap but good stuff. This is from her website but this is one of my hats.
The guy in the photo desperately needs a "Mayor" sash.
My favourite all-purpose winter hat is a Tilley TW2 Classic Winter Hat. I have one in Charcoal.
Made mostly of wool, and has a hint of fedora in its appearance, so it looks classy enough for any occasion.
View attachment 717966
It has concealed earflaps and (though not shown) a separate smaller flap for your forehead too.
View attachment 717967
I gotta have some kind of bill or brim so as to keep falling snow off my glasses.
It's soft enough that you can stuff it into a large jacket pocket, if needed, and it doesn't take long to get it's shape back.
For more active occasions like shoveling or snowshoeing I'll go with a wool Jeep Cap, which my wife bought for me on Amazon. I don't want to sweat up the Tilley.
View attachment 717968