I would spend longer in Montreal than in Quebec City, but that's just personal taste. There should be indoor cultural events in both places. As for the great out-of-doors, the amount of snow cannot be guaranteed (nor can it in Chicago at that time of year.) Both cities have useful tourist info on-line. Here is the provincial site http://www.bonjourquebec.com/qc-en/veneznousrencontrer0.html The cities are at http://www.quebecregion.com/en and http://www.tourisme-montreal.org/ The train is at www.viarail.ca Buy tickets soon as the demand is high around the holidays.
Along with the usual international airlines, you will find connections on Porter Airlines which flies out of Chicago to both cities, requiring a stop at Toronto's downtown "Island airport" known now as Billy Bishop. Porter flies only propeller-driven aircraft which are new and comfortable but also subject to more turbulence than jets.

Between the two cities, you can easily fill 6 nights, even in the bitterly cold winters up there. As the above poster mentioned, spending at least as much time in Montreal would be a good idea. Even though Quebec City is very scenic, it is fairly small. Montreal is a much bigger city, with a lot more to explore. Quebec City is a place to walk the cobblestoned streets, take lots of pictures, get warmed up in a creperie, and x-c ski on the Plains of Abraham. The Museum of Civilization is a fun place to spend a few hours.
Montreal is very rich in ethnic neighborhoods (Italian, Jewish, African, Portugueese, etc), nightlife, shopping, and world class dining. You can peruse the byob restaurants and funky shops on the Plateau, explore the Old Montreal and the waterfront, and shop the big department stores in the downtown. The Fine Arts Museum is a great place to keep warm on a bitter afternoon. There are plenty of outdoor activities in the parks and on the trails like x-c skiing, snowshoeing, etc.