The non-instrument rated pilot crashed about 3 hours after taking off with 4 1/2 hours of fuel on board. He crashed while attempting an off-airport landing in a large field. The field was located less than halfway to his destination. The sheriff reported minimum visibility with snow and freezing rain. The occupants received only minor injuries, but the plane was destroyed by impact and ground fire. An examination of the wreckage revealed no evidence of a pre-impact malfunction or failure of the engine or inflight fire. The pilot provided the following account: He was cruising above an overcast at 17,500 feet when the left engine began cutting out and forced him to descend through the clouds. He descended to VFR conditions at 1,200 feet AGL over snow-covered terrain and determined his location by viewing a water tower. He then elected to land in a field when he saw smoke and fire coming from the engine cowling. While landing, the left wing dropped and touched down first.