I moved from CA to NY for law school over 3 years ago, and I created a similar thread back then! Time flies...haha.
Since relocating to NY, I've found that hats & scarves are lifesavers against the windchill. Nobody wears hats in CA for warmth, but wearing one makes a world of a difference in very cold weather. Keep in mind, it's going to be the windchill that will freeze you and not so much the bare temperature because the wind seeps into your clothing. Hence, as others have posted already, layering to minimize windchill is paramount. Afterall, you are moving to a city that is nicked named "the Windy City"!!
As for jackets, I don't own a down jacket, but I own several heavy duty wool & cashmere blend coats that all cover the bum area. If you're getting a wool jacket, make sure it's insulated (also known as thinsulate) so you'll be able to retain the heat.