I live north of Toronto and we might have comparable weather in the winter with Chicago (maybe a bit more snow and a bit colder...)
The problem with a lot of "all season" tires or summer tires for that matter is that the tread blocks literally freeze in cold weather - we're talking below freezing and colder. I've had some scarey experiences with my summer tires - FireHawk SZ50's once the temp's get low in November and December. They just don't grip at all...
My tire shop owner basically scoffed at "all seasons" for Canadian Winter saying that there ain't no such thing - get Winter tires for Winter (at least when there's snow...
A few years back I bought a second set of wheels and now have a set of 15" (you could use 16's) with 4 Bridestone Blizzaks for winter, and a set of 17" wheels with the FireHawks for Summer. I usuallu change over to the winter wheels by mid/late November.
This setup has kept me on the raod in Canadian winter for the last 4 years, and is way more drivable than the all season Goodyears that were on the car before.
Hope this helps
Cheers Keith