The student pilot had been planning to take his long solo cross country flight for a number of days. On the accident date, the student obtained a computer weather briefing. The weather for the route of flight was forecasted to have a chance of snow showers. Weather at the departure airport was light snow showers during the time of the briefing and predeparture discussion the student had with his instructor. The student departed on the solo cross country flight during very light snow showers. Approximately 8 to 10 minutes after the student departed on his flight, the instructor called him on the radio. The instructor asked the student how the weather was. The student replied the visibility was three miles. Shortly after this conversation, the student called the airport and stated he was lost and having difficulty. The airport manager, a non-pilot, told the student to make a 180 degree turn and return to the airport. A ground witness stated he heard an airplane fly overhead two times during very heavy snow showers. During the second pass, the witness stated he heard a vacillating engine sound and a loud crash sound. The wreckage was located approximately 30 minutes after the witness heard the engine sounds.