I ended up circling the same city block looking for a non-existent logging museum. Sadly, school has just let out and I instead looked like a tired, unshaven man scouting the best place to offer a child a roofied Kit Kat.
I was about to give up the ghost when a man breaking up the ice on his driveway with an auger told me I was nowhere near the correct location of the museum. I eventually found the logging museum (closed for winter) and with no Hodag statue in sight.
I was definitely losing my religion at this point, and was aimlessly driving around the suprisingly large town looking for an exit toward Eagle River when--voila!--I turned a corner and there she was. And not only did I find the statue, but there was another Benz in the parking lot! (That's number two!) I suddenly felt a little less alone, at least until the woman on a cig break outside the Chamber of Commerce asked what I was doing with that trophy.
My explanation made even me feel a little sorry for myself. But she was kind enough to pretend that driving around the state following high school hockey was a great idea. Such kind people here in Wisconsin.