Of the threads I find by googling around, Midway seems to be better than O’Hare in terms of less likelihood of winter weather delays. I would need to find a Chicago native to confirm this, however.
Reference: http://www.city-data.com/forum/chicago/124947-ohare-vs-midway.html,
http://www.tripadvisor.com/Travel-g35805-c80962/Chicago:Illinois:Tips.For.Ohare.Travelers.html,
http://www.kellogg.northwestern.edu/serial/purplepages/travel.aspx.