Houghton would be a tough winter drive from either Wausau or Green Bay, although Green Bay would tend to have somewhat larger planes. If you're driving the last rural distance, you could also aim for Duluth. Madison or Milwaukee would cut a couple hours of interstate driving (Green Bay and Wausau a bit more), but my concern would be the drive in/near the UP, including close to the whole way from Green Bay or Wausau as IIRC from either one, the highway ends about an hour north. Of course if the OP's real destination in the UP isn't that close to Houghton, this point might be moot.

BTW I just tried to look at driving conditions road reports and in MN, all major roads northeast of Duluth (which the OP wouldn't be using, but it gives an idea of general conditions across the state line) are still totally snow covered. The area around Houghton would have gotten the same weather system a bit later, so I would not want to be driving in that area today. OP should also monitor weather reports for the next winter storm expected to hit the area.

When I last checked, DL did serve Houghton, so there wouldn't be a need to drive the last sector as Often1 suggested above, just to get where you're going from that airport. Of course, DL serves Gren Bay, Duluth, Madison, Milwaukee, etc. although not nonstop from ORD.