On a flight from Glenn Falls to Lake Placid, NY, the non-instrument rated pilot encountered deteriorating weather. ATC data showed this occurred over mountainous terrain at about 1517 EST near Burlington, VT. The pilot elected to return to Glenn Falls. At about 1521, he told the controller he had Lake Champlain in view. The lake was mostly frozen over with approximately 3 ft of snow on the surface. About 5 minutes later, radar service was terminated, and the pilot acknowledged. No further transmissions by the pilot were received. Wreckage was found on the frozen surface of Lake Champlain near the Vermont shore. An exam revealed the airplane had impacted the ice in a right wing low attitude. It was extensively damaged, but no preimpact anomalies of the airframe or engine were found. A witness on the New York lake shore saw an airplane at about the time of the accident, in a steep left turn at about 250 ft AGL. He stated he lost sight of the airplane due to the bad weather. He also stated that at the time he saw the airplane, a severe blizzard was moving across the area and it lasted about 15 minutes.