Tough call, since I've never done well in winter.
But, massive carp I am sure are present year round in the Chicago harbors. Likely the Chicago river as well. Although I'm not sure where to recommend. I can say, the north loop stretch during extended cold fronts freezes over, so that's a no-go, but the rest flows quickly enough that it never seems to totally freeze.
Guys on here and other forums talk about the harbors freezing over, and then sneaking out to open up barely-frozen holes from previous fishermen. Might be an option, I've never tried.
I will tell you what, if anyone wants to get together an ice fishing expedition I am deeply curious about eating some Burbot. I'd be happy to gear up a bit, and will be local to Chicago until early January.