I am a dedicated Chicago winter biker and only stay off the bike path when there is too much ice. (I'm too old for those kinds of falls.)

The lakefront path is Chicago's jewel, and Lincoln Park is at the heart of it. So long as the temperature is above 40 degrees, you should be fine with a few layers, a wind jacket, decent gloves, head cover, and shoe covers, unless the wind is off the Lake at 20+ mph. (We may not have hills but we have the wind off the Lake.)

Try the Lincoln Park Zoo; it is incredibly quiet in the winter. The Peggy Notebart Nature Museum in Lincoln Park is geared to kids, but the butterfly exhibit is worth the price of admission. If you like to bird watch, Chicago is a major stopping point for shore birds in the winter (lots of gulls, terns, and waterfowl).

Enjoy!