I always went camping at White Pines state park located near Dixon, IL (about a two hour drive from the city). It is sort of pine trees in the middle of the corn fields, so the hiking isn’t fabulous, but I like the camp grounds. You’ll have to check to see if they allow winter camping, though. And no, you won’t need snow chains. In fact, I don’t think Illinois allows chains. Another place is Starved Rock near Utica, IL. That is a really pretty place, but again, check to see if they have winter camping. I just checked: there is camping year round at white pines. Hope this helps.