The private pilot reported that before landing on the frozen snow-covered lake in a ski-equipped airplane, he intended to do a touch-and-go landing to check the snow conditions. He said that variable and gusty north-northwesterly winds required him to depart into an area of rising, tree-covered terrain. After landing to the northwest, he added full engine power, and the airplane became airborne, but would not climb fast enough to out climb the rising terrain. In the pilot's written statement to the NTSB he stated, in part: "Failed to fully recognize situation in time to abort departure..." The pilot indicated that the airplane collided with tree-covered terrain at the departure end of the lake. The airplane sustained substantial damage to the wings, fuselage, and empennage. The pilot indicated that there were no preaccident mechanical problems with the airplane.