People enjoy all sorts of winter sports even though it is really cold outside.
So there is no reason not to play tennis on a cold day, as long as the court is in good condition.
I play right down to 32 degrees. There should be plenty of afternoons in Chicago when the temperature gets that high over the next few months.
Warm up beforehand with a little jog around the court, some agility drills, practice swings, a reasonably long pre match rally and try to keeps the game moving.
Wear nylon and fleece that will wick sweat away. Shed clothing as you warm up so you don't overheat. (You can always put another thin layer back on.) Buy some football receiver's gloves. Make sure your tennis shoes have good traction (Asics Gel Resolution II's have a slightly softer sole that doesn't seem to harden up as much as many others.) You may find that non pressurised balls bounce better in the cold than regular pressurised ball. Be prepared to string your racquet slightly looser, use a softer string, and still have to restring more often from broken strings.
You're a Bears fan.
Be a man.