Always! I can't wear toques; my hair is fine and slippery and they pop right off the top of my head. Usually I wear a beret, or sometimes a headband to protect my ears better.
I also have a sheepskin-lined brimmed hat that's lovely for warmth in the depths of January, but the black has faded from sun exposure in the rear window, and I haven't figured out how to fix that.
In milder temps and minimal wind I'll sometimes wear a fedora or a more ladylike style of brimmed hat.
Something about the width of my shoulder demands a wide brim... Like, if I wear a 3" brim it almost disappears, looks like a bucket hat with a 1" brim. So hats need careful trying on, and also consideration to whether I'm blocking the view of someone behind me.