The pilot reported that prior to landing, he performed two low level passes to determine a safe landing area on the frozen lake. During the landing, the left landing gear ski touched down and the pilot heard a bang as the left ski impacted a snow covered raised ice ridge. The pilot slowed the airplane for the remaining landing and it came to rest upright. Examination of the airplane revealed that the landing gear box structure was bent and the bulkheads were damaged. No mechanical anomalies were noted with the airplane. The pilot reported that he should have landed the airplane in the middle of lake which likely would have had less slush and rough ice.