If you're wanting to wrap it around your neck and have it sit over your clothes you can go for a heavier/thicker wool scarves. Lastly, if you are wanting to wear it under a jacket and wrap it around your neck, go for the fine cotton or silk scarves including the blends.
I think winter wear is communal. You get some gloves and a scarf from a lost-and-found, wash them, wear them for a while until you lose them. Then somebody else does the same thing.'