Snow tires for winter and summer tires on the new rims for the rest of the year.
Not sure if you are new to the area, but if you are, you'll find out quickly that Chicago has the most fucked up weather of any area. I'll be putting my winters on within the next couple weeks most likely and won't take them off until late Feb to early March. With this spread, it works out to about 50/50 usage between winter and summer tires.
I've never driven in the winter in all season, but I do know snow tires are amazing.
And welcome to the forum. Post up in here, assuming you are not easily offended and okay with strangers talking about your junk: http://www.e90post.com/forums/showthread.php?t=727626