Buckhorn State Park (about 1 hour 45 min drive from Madison) has a few backpack camping sites. It's not truly backcountry, but it might be the best you can do in the area, and there are many hiking trails worth exploring.http://www.dnr.state.wi.us/org/LAND/par ... amping.htm
I haven't camped those sites, but did walk to one. It was maybe a mile from the camp roads. The sites are fairly isolated from one another, but there are portable toilets that a cluster of sites will share.
From this site
Sites 8, 9, and 16 are available for winter camping on a 1st come / 1st served basis, when not on reservations. Except where noted below, all other sites are closed to camping, when not on reservations.
I believe those are backpacking sites. Regardless, I'd give them a call to make sure that information is current. Since it's a state park, be prepared to pay for an annual vehicle sticker or daily pass.
The park is quite beautiful, so I'd keep it as a candidate, even if you don't end up there this weekend.