General Carlessness guide to winter [cycling] in Chicago
The thing about winter in Chicago is that it sucks. Bicycling in winter isn't a whole lot of fun, and anyone who tells you otherwise is clinging to their delusion in order to survive, lest they succumb to a greater madness. But you know what, walking in winter also sucks, as does cramming onto a stuffy train in winter, waiting for the bus in winter, and digging your car out of the snow only to find that it won't start in winter. So all things considered, riding a bike is really no more unbearable than any other form of transportation.
This will be only my second (noncontinuous) complete winter as an all-season bike commuter, but it will be my tenth as a car-free city dweller, and I assure you that a lot of the special gear you'll need for winter bike commuting are articles that, if you ask me, should already be included in your wardrobe of "regular" clothes. In fact, they probably are.
Coverings for the head, face, and hands. At the more general end of the spectrum are your basic hats, scarves, and mittens or gloves. I usually prefer earmuffs and an insulated hood to a hat, but it does the same thing. Get the warmest gloves/mittens you can find. They will be ugly; just accept this. The point at which you are biking often enough to develop a soul-crushing hatred of wet fleece is the point at which you should consider getting a balaclava, but until then you can probably skip it unless somebody gives you one. Or you succumb to Bicycle Movement peer pressure. Whichever. In the meantime, a simple fleece scarf will suffice.
A waterproof top layer with ample butt coverage. That cute hip-length jacket is going to ride up as soon as you bend over your handlebars, so maybe that's why you haven't considered winter biking a viable option. Trust me, a longer coat will keep you so much warmer no matter what you're doing, so you may as well get one. Make sure it's waterproof. Don't trust anything labeled "water resistant" because it will probably only keep you dry in the event of fog. Oh, and don't use liquid laundry detergent on your outerwear; it compromises the waterproofing material.
Insulated waterproof boots. You'll thank me later.
Socks. Every winter I'm amazed by the number of people who don't seem to wear socks, or at least not much in the way of socks. Wool will keep you warm. Acrylic might. Cotton will not. Nylon most definitely will not.
A huge bag. You need to keep your hat, scarf, gloves, and extra socks somewhere, you know.