At about 1100 Alaska time, the ski-equipped airplane sustained substantial damage after landing on a snow-covered lake during a Part 135 VFR passenger flight. The commercial pilot and passenger were not injured. Visual conditions prevailed. The pilot later said he departed with the airplanes oil cooler cover in place, but engine temperature increased significantly, and he decided to land on a snow-covered lake to remove the cover. While the pilot was laying down tracks in the snow to aid in the takeoff, the airplanes skis hit a hidden ridge in the snow. The pilot examined the airplane and found a fuselage frame tube had broken near the right main landing gear attachment. He called for another airplane to pick up his passenger.