The commercial certificated pilot reported he is conducting research at the University of Alaska, Fairbanks. As part of his research, the pilot was conducting a survey of caribou. The pilot said he landed on the surface of a frozen lake in a tundra tire equipped airplane, and was taxiing toward the shore. As the airplane neared the shoreline, the airplane tires broke through the ice. The airplane received damage to the right landing gear strut, and the right wing lift strut was bent.