It's absolutely not an answer to your question, but 2 miles is not a very long distance. You could fast-walk it on some days when it's really bad and you don't want to take your bike. I walked 3 km (about 1.9 miles) each way to work in the Montreal winter. Not quite as wet as Chicago perhaps, but often very cold, very humid, and very slushy. Having good boots made it work. It took me just over half an hour, and was very invigorating.

For the other days... you might be inspired by the Chicago Bike Winter folks:
http://bikewinter.org/main.php