The pilot departed on an instrument flight with what he reported as an estimated 26 gallons of fuel on board, or 1.6 hours of flying time. The destination airport was an estimated 1 hour and 35 minutes flying time away. Approximately 14 minutes into the flight, at 11,000 feet, the pilot requested to land at a closer airport for fuel. Approximately two and one half miles from the alternate airport the engine failed. The pilot attempted a gear down landing to a snow covered field. On final approach the airplane struck a tree and impacted the ground. According to computations made with documents provided by the pilot, which included his anticipatory fuel log, the pilot departed on the flight with an estimated 13.5 gallons of fuel, which according to the pilot's estimate of 17 gallons per hour fuel burn, gave him approximately 48 minutes of fuel in the tanks at take-off. Fuel exhaustion occurred approximately 50 minutes into the flight.