Wear layers. A scarf makes a huge difference. Probably larger than you would think.
Chicago will probably get a "polar vortex" in February or March. It will be a week of really cold weather and then it will be over. You'll probably find that November and December are warmer than you expected. January is a bit dreary, but only because of the reduced daylight hours (compared to LA). Chicago is just a bit further north than NYC, but compared to Paris or London it gets a lot more winter daylight.
The think I've noticed about winter since moving to Chicago is that the really sunny days are the coldest and the cloudy days are warmer. If you've got large south-facing windows, you might need to close the shades or even open the window slightly when it is really cold. That sun can be intense!