The non-instrument rated pilot was advised before departing on a cross country flight that VFR flight was not recommended. He departed without filing a flight plan. Before reaching an intermediate stop, he obtained an updated weather briefing for the local area and his final destination. After refueling, he took off and proceeded toward his destination which was approximately 156 nm to the east. A large slow moving frontal system was positioned over northcentral Texas at the time. The pilot's route of flight was along the southern boundary of the front. Light drizzle, fog, and low ceilings existed along the route of flight. Subsequently, the airplane entered a descent and crashed approximately 63 miles southwest of the destination airport after about 3 hours and 20 minutes of flight. No preimpact part failure or malfunction of the airplane was found, though it was badly damaged during impact. Several local people stated there was low ceilings, fog and drizzle at the time of the accident.