On April 6, 1993, at approximately 0740 mountain daylight time (MDT), a Piper PA 24, N5541P, impacted the terrain after a loss of power while on ILS final at Natrona County International Airport, Casper, Wyoming. The FAA certificated flight instructor, the FAA certificated private pilot, and their passenger were not injured, but the aircraft sustained substantial damage. The pilot, who was on a personal pleasure flight, departed Cumberland Municipal Airport, Cumberland, Wisconsin just over five hours earlier. He had originally filed an IFR flight plan for Rapid City, South Dakota, but while en route, the destination was changed to Casper Wyoming. The ELT was activated upon impact, and was turned off at the scene. According to the instructor pilot, he had been asked by the owner of the aircraft to accompany him on the flight because of the potential for bad weather. The night before the flight, the instructor asked the owner, who was not instrument rated, to check the weather, and to plan and file an IFR flight plan. According to the instructor pilot, prior to departure the owner told him that the latest forecast winds would be about 90 degrees to the intended course at about five knots. The morning of the flight, about 15 minutes prior to takeoff, the owner fueled the aircraft and received an IFR clearance for departure from the uncontrolled airport. The instructor pilot said the he did not personally make a visual inspection of the fuel level after the owner had fueled the aircraft. According to the instructor pilot, the flight initially leveled at 10,000 feet, but then climbed to 12,000 feet in order to stay above the clouds, in which light icing had been reported. He also said that, "We encountered headwinds of 20 to 30 knots along the entire route." When the flight was about 15 minutes from Rapid City, the instructor pilot received current weather for that destination, and also for Casper, Wyoming. According to the instructor pilot, the weather at that time for Rapid City was a 400 foot ceiling with a visibility of one mile. Although the instructor pilot stated that the ILS was inoperative at the time he received the weather report, the current ceiling at Rapid City was higher than the published Minimum Descent Altitude (MDA) of 282 feet Height Above Touchdown (HAT), and the visibility was greater than the published one half mile required for the available localizer only approach at Rapid City. Although the instructor pilot's written statement says that the Casper weather he received at this same time was "...reported at 400FT and 1 mile visibility," the FAA inspector who responded to the scene said that he had listened to the audio tapes of the pilot's conversation with both Center and Flight Service, and that the weather they gave him was 200 feet obscured, visibility variable from one eighth to one half mile, heavy snow and fog. The published minimums for the ILS at Casper were a Decision Height (DH) of 200 feet above the touchdown zone, and a one half mile visibility. After receiving these reports, the instructor pilot elected not to land at the original Rapid City destination, but instead refiled for a final destination of Casper. At the time of his refiling, no alternate was designated. While en route to Casper, the flight continued to encounter the 20 to 30 knot headwinds, and once again had to climb higher, to 14,000 feet, to avoid icing in the clouds. While on the approach to Casper, the aircraft's engine began to run rough and eventually quit. After a gear up landing in a snow covered valley, the occupants eventually made their way to a nearby road. According to the FAA inspector who responded to the scene of the accident, there was no fuel remaining in the aircraft's tanks, and there was no evidence of fuel spills or leaks on the fresh snow. According to the instructor pilot, after the accident the owner informed him that "... he thought he could have gotten three or four more gallons in the fuel tanks..." prior to departure. This same inspector stated that after interviewing both the owner and the instructor pilot, he had determined that the original desired destination had been Casper, Wyoming. But, according to the inspector, the instructor pilot's original decision had been to fly to the filed Rapid City destination, refuel, check the weather, and then continue on to Casper if conditions permitted. Instead, according to the FAA inspector, the instructor pilot, who had experienced continuous headwinds while en route, and was facing reported weather that fluctuated below minimums at his desired destination, continued on toward Casper until reaching a point where no fuel remained in the aircraft's fuel system.