CHI84LA329

Drg a x-country flt at 4500 ft, eng began sputtering. Plt adusted the mix; then applied carb heat, but rprtdly for only a short time. Eng contd operg, but at reduced pwr. Acft lost alt & dscndd into clds, but the plt was able to lvl at APRX500' AGL. He elected to divert, called Wausau (auw) fss, declared an emerg & rqstd assist. Fss had no df equip. The acftwas too low for radar id & its adf was inop. Plt was unsure of his psn, so the fss specialist (fsss) tried to assist by using VOR orientation procedures. After the plt tuned in the stevens pt (ste) VOR & rprtd hdg 10 deg (presumably to the VOR), the fsss erroneously told him he was btn ste & auw, when actually, he was south of both vor's & close to the ste arpt. The fsss told the plt to fly to auw VOR (n of ste). After the acft passed north of ste, the fsss id'd its psn nr alake just south of auw & told the plt to cont to the VOR. Moments bfr rdo contact was lost, the plt rprtd 011 deg to thevor stn. The acft hit trees nr mtn top aprx 7 mi nw of the VOR. No preimpact mechanical prblm fnd. Carb ice cond rprtd.