I live about 20 miles SW of Chicago, not exactly a hiking mecca. I do a lot of forest preserve hiking in the winter in places like Black Partridge Woods, Waterfall Glen, Cap Sauer Holdings, and Red Gate Woods. The latter has historical significance. A facility in those woods was the forerunner to the nearby Argonne National Laboratory. The world's first nuclear reactor was moved from the University of Chicago to those remote woods, and was buried there when the facility was closed in 1956. There is a granite monument in a clearing, which I first stumbled across circa 1969 when a friend and I decided to go for a hike rather than fish with his dad and older brother at Saganashkee Slough on the other side of 107th St.
I like hiking in the colder weather when the trails are firm rather than muddy, the off-trail routes are less overgrown, and bugs are absent. A little-known waterfall in a rocky canyon runs through a creek between Bluff Rd and the Hindu Temple of Greater Chicago on the east side of Lemont Rd, just north of the bridge from Lemont. That trailhead hooks up with the 9-mile Waterfall Glen bike path that encircles Argonne Natl Lab.