My D has a wool pea coat and she layers it with a fleece jacket and/or sweater.
On extremely cold days (sub zero) she wears her puffy jacket from Old Navy. It was not that expensive. You can probably order it online and have it shipped to dorm.
We got a pair of insulated ladies Wolverine boots (she doesn’t like the duck boot look) from Amazon and a few pair of merino wool socks from LL bean (the machine washable kind, but I would not put them in dryer)
Personally, I am not a fan of the coats with a shell and a zip out lining, unless perhaps for travel. At least with the one I have, when you remove the lining you are left with a much over-sized shell. It could be ok for travel but I think for years of everyday wear it makes more sense to just get jackets of the weights you need.
Regarding boots, make sure the fit allows for thick socks.
I go to college in Pittsburgh. I have two wool coats (one peacoat and one duffel coat) that I wear most often—the duffel coat is especially thick and warm— as well as a lighter-weight North Face down coat/jacket, which I didn’t find myself wearing too often. I layer with warm sweaters and usually wear a hat, gloves, and scarf. Boots (I have a few pairs of leather boots and a pair of Sorel snow boots) are your best friend, as are Smartwool socks. Cold ankles are no fun.