You gotta keep your head warm too! Hoods won't do it enough so go grab a tuque like this one at American Apparel (because I basically live there).
Wrap up your neck! Again, this seems like a no brainer but you gotta keep it covered. It's a very sensitive and thin skinned area on your body so you have to keep it covered so that it doesn't make you cold.
NOW to kick dryness in the butt, keep your skin moisturized and your lips unchapped! My faves are Aveeno moisterizer, I've been using it for years and it always protects me from gross, peeling skin. For me, there is NOTHING WORSE than dry lips!! Burt's Bees is my saviour in dry season.
Try them out, and keep covered!! Also let me know in the comments what you use to keep warm and to stay happy during the cold, dry winter!