The student pilot was returning at night on the last leg of her long solo cross country. According to the FAA, the pilot departed Lancaster Airport at 1758 EST and had received a preflight briefing that indicated flight precautions for IFR conditions. The instructor reported that the original trip planned by the student was cancelled due to IFR conditions on that route. She changed her route and as instructed, she called him from Lancaster and reported her location. She also advised him that the weather was VFR for her return trip. The instructor stated that he told the student that if any uncertainty existed once she became airborne, she should land. Radar data obtained from the FAA showed the airplane at 900 feet making several turns. According to witnesses the airplane was seen through the fog and drizzle circling the area. The airplane collided with trees in a heavily wooded area and then became inverted. Examination of the airplane did not disclose evidence of mechanical malfunction.