The commercial pilot reported that he was landing on the frozen snow-covered lake in a ski-equipped airplane. During the landing roll the airplane's main landing gear skis encountered a snowdrift, which stripped the nuts that connect the skis to the main landing gear axle. Both skis separated and the airplane's left main landing gear leg collapsed. The left wing struck the snow-covered frozen lake. The airplane sustained substantial damage to the left wing and fuselage. The pilot said there were no preaccident mechanical problems with the airplane, and noted in his report to the NTSB that he should have inspected the landing site before landing, then selected a better area to land on.