Admittedly, I haven't ridden along Chicago's notoriously windy lakefront, but from my experience with cold weather riding, how "fun" it is kind of depends on the day. I don't mind the cold too much if it's at least a sunny day. That lightens my mood quite a bit. It's hard to get too motivated to ride--at least for me--if the day is both dreary and cold.
In any event, you can dress for it. Layers, a windproof jacket, head/face covering, winter gloves, wool socks and the like. Count on being a bit cold when you start and then warming up as the ride progresses. One rule of thumb that I stick to. If I'm warm enough for the first 10 minutes of the ride, I'm overdressed.
Good luck. With or without a ride, enjoy Chicago. It's a great city.
Live with intention. Walk to the edge. Listen hard. Practice wellness. Play with abandon. Laugh. Choose with no regret. Continue to learn. Appreciate your friends. Do what you love. Live as if this is all there is.
--Mary Anne Radmacher