First of all, the city rarely shuts down. I remember one time in the last 5 years where govt, etc. was shut down for a day. But I could still put on my boots and walk 3 blocks to my neighborhood pub for dinner! ORD is another story though. December is a pretty safe month however. Most years we don't have lasting snow until after Christmas. There's always the chance you'll hit a freak storm that will close ORD for a few hours or a day, but there's probably less chance of that in December than a thunderstorm in June closing it.
That said, it's possible that it will be cold. Sometimes mid-December is 45 degrees, and sometimes (less often) it's 4 or 5 degrees.
Our average temp is high 30's in December.