THE PRIVATE PILOT WAS ON AN IFR FLIGHT TO ST. LOUIS. WHILE APPROACHING THE NASHVILLE, TN. AREA, HE ENCOUNTERED ICING CONDITIONS, AND REQUESTED A DESCENT. THE ICING PERSISTED, SO HE REQUESTED AN ILS APPROACH TO NASHVILLE. THE AIRCRAFT CRASHED ABOUT 12 MILES SSW OF THE NASHVILLE AIRPORT, AFTER THE PILOT REPORTED THAT HE HAD LOST POWER, AND WAS STALLING. AN INSPECTION OF THE WRECKAGE REVEALED THAT THE LEFT, AUXILIARY FUEL TANK WAS EMPTY OF FUEL, AND THE FUEL SELECTOR VALVE WAS STILL IN THE 'LEFT AUX' TANK POSITION. NO EVIDENCE OF PRE-EXISTING MECHANICAL MALFUNCTION OR FAILURE WAS FOUND.