THE ACFT COLLIDED WITH THE GROUND DURING AN ILS APPROACH. THE WEATHER WAS IMC AT THE TIME AND AN IFR FLT PLAN WAS FILED.THE PILOT WAS INSTRUMENT RATED AND HAD RECEIVED A WEATHER BRIEFING WHICH FORECAST ICING AND FREEZING DRIZZLE. THE PILOT TOLD THE WEATHER BRIEFER HE DID NOT THINK IT SOUNDED TOO BAD. THE FSS BRIEFER STATED ITS NOT THAT GREAT. THE PILOT ELECTED TO GO AND AFTER CLIMBING TO 8000 FT BEGAN TO GET STRUCTURAL ICING. LOWER ALT WAS TRIED WITHOUT SUCCESS IN AVOIDING ICING. AT THE SUGGESTION OF GREEN BAY ATCT THE PILOT ACCEPTED VECTORS TO AN ILS APPROACH TO AUSTIN STRAUBEL ARPT 50 MINUTES AFTER INITIAL DEPARTURE. THE PLT COULD NOT SEE THE RWY AT DECISION HEIGHT DUE TO WINDSHIELD ICE. VECTORSWERE GIVEN FOR ANOTHER APPROACH. THE PLT SAID HE HOPED TO SEE OUT OF THE SIDE WINDOW. AT DECISION HEIGHT HE SAW THE RWY TO THE LEFT OUT OF SIDE WINDOW. HE SAID HE TURNED LEFT AND THE RIGHT WING DROPPED AND HE CAME DOWN. THE ACFT CAME TO REST 500 FT SHORT OF THE RWY AND 100 TO 150 FT RIGHT OF CENTERLINE.