I live in SoCal now, so not really cold here but I commuted by bike in St. Louis for many years, so I learned to dress for cold weather. The one thing I would add to the above is that wool is your friend (cycling specific or not).
I still use wool socks, even here in SoCal (Woolie Boolies are my favorite!). Anyway, wool tops, ear warmers, etc. keep you warm (even when they are wet) wick moisture well and don't smell as bad as quickly as other materials. I use wool knee warmers and arm warmers even in this environment.
Sheep have been developing wool for thousands of years and in my opinion, they got it right!
Rick / OCRR