Winter hats

It is a well known fact that you lose most of your bodyheat through your head. Obviously, which hat you wear will make a big difference to how warm and happy you are, climbing, walking or sleeping in cold weather.

Tom HS and I were climbing our joint first winter route, boomerang gully in Glencoe. I was wearing my helmet and no hat, Tom had a wooly hat and no helmet. We set off up the route, pitching the technical step then moving together for the rest. At the time I had fairly long, curly hair and when we reached the top the moisture in the air had frozen my hair into a solid, heavy lump. This remained frozen till we reached the bus when it thawed, wetting my clothes.
 To give an idea of how cold it was that day, my bottle of Irn Bru (google it if you don't know) froze.
 A while later I was winter climbing at Lochnagar with Chris. We climbed a buttress, at around the same grade as boomerang gully but a lot longer. Stuck on belays for extended periods of time I kept warm by wearing a fleece hat underneath my helmet and having a belay jacket on over my waterproofs. Though soaked by the end of the experience I was warm and comfortable.

There are far more types of hat on the market than you would think.

Wooly hats...like the one your granny knitted you. Fairly warm, not windproof, breathable.
Fleece hats....I like mine as it is not too warm, meaning I don't sweat, and is fairly thin so it is comfy under a helmet.
Insulated hats...typically the insulation is concentrated at the top. Very warm.
Down hats...I have never seen one but if they work as well as down jackets they must be roasting.

Down jackets/synthetic jackets often have their own hoods. These usually go over the helmet, leaving more room for air to get in.out.

Windproof, softshell-like hats are light and increasingly popular.
Beanie hats are popular amongst boulderers. So, though, is hanging about in caves.

All in all, it would be hard to go far wrong.

Balaclavas are great. I had one when at school for winter and have not worn one since, but in more extreme conditions these would save the inevitable chilled neck and face.

That said, perhaps just growing a mane of hair and a beard will suffice.