The two instrument rated pilots departed for a night IFR cross country flight into forecast icing conditions in a carburated Mooney M20C. The pilots received three weather briefings in which they were advised of light to moderate mixed icing conditions from the 6,000 foot freezing level to 18,000. The owner pilot in the right seat held a commercial and instructor's certificate for single engine land airplanes. The left seat pilot held a private pilot's certificate for single engine land. They were cruising at 12,000 feet. They reported experiencing light rime icing conditions in a radio exchange to FSS. The pilot requested a climb to 14,000 feet, and, during the climb, requested a descent back to 12,000 feet. Shortly thereafter, he stated that he had engine problems and requested vectors to the nearest airport. The flight was given radar vectors toward the two airports in Redding. Ten minutes into the emergency descent the pilot stated that they were still IMC but "the icing's melted off." During the descent they stated that they had no engine power. The aircraft collided with power lines about 1.6 miles from the Benton Redding airport. The airplane was not approved for flight in known icing conditions.