Very important question for Kellogg and Chicago students

Not from Chicago but from the north east and ski a lot. The key is layers but beyond that if you are looking for a very warm coat go with down. Now you want something longer and that has a hood. The North Face makes good stuff but you are going to pay a premium for the name generally, and honestly down coats often look very similar. A good bet is LL Bean, good quality and an amazing return policy. Also the sierra trading post can be a great spot to find really good deals.

Look for something along the lines of this.
https://www.llbean.com/webapp/wcs/stores/servlet/CategoryDisplay?page=goose-down-hooded-parka&categoryId=51588&storeId=1&catalogId=1&langId=-1&parentCategory=502788&cat4=502786&shop_method=pp&feat=502788-tn

You will want a nice tight knit hat with fleece lining, a scarf can be a nice addition when its nice and windy. Good gloves are important too, look for something with removable liners, that allows you to wash them and to allow you to vary layers there. Oh mittens are way warmer. Buy ski/winter hiking socks too.

Boots are key too, when its snowy you are going to want to get something waterproof and warm. A good bet are bean boots. There are a several versions, they are reasonably priced compared to most brands. You could get a pair of uggs that are the same thing for 250 or beans for 100.

https://www.llbean.com/webapp/wcs/stores/servlet/CategoryDisplay?categoryId=35374&storeId=1&catalogId=1&langId=-1&feat=43359-ppxs&dds=y