The boat tours stop in mid-November. Which is fine, as JBord said, being on the river could be terribly cold and windy. Other CAF tours (walking, bus, L) run all winter. Our worst weather tends to be more toward late January-early February. Prepare for cold, don't be surprised if it's in the 50s. If it's horrible, take a tour of the pedway.
December and February are pretty comparable for snowfall and avg temperatures:
https://en.wikipedia.org/wiki/Chicago#Climate
December is also darker.
But I echo others on this thread that as long as you are expecting it to be winter, it's a fine time to visit. Bring a good coat. You'll miss out on hanging out in lakefront parks, but museums, restaurants, architecture, etc. are all still here.