The operator reported that the pilot had diverted to an alternate airport due to weather. As the flight approached the alternate airport, the weather had deteriorated, and the pilot requested a Special VFR clearance. The flight continued to follow the lake shoreline and the pilot recalled circling once while waiting for the clearance. Prior to reaching “the mouth of the river”, the pilot made the decision to divert to another alternate airport, due to the visibility getting worse as they approached the airport. As the pilot began to make an approximate 20° right hand turn over the frozen, snow-covered lake, he noticed the airplane was losing altitude and remembers increasing power and pitch, around this point he “switched to instruments”. The passenger recalled looking to his right and remarked it was like looking at a “white sheet of paper” with the sky blending with the frozen lake. Moments later, the airplane impacted the snow-covered ice while in the turn to the right. The airplane sustained substantial damage to the wings, fuselage, and empennage. The operator reported that there were no mechanical failures or malfunctions with the airplane that would have precluded normal operation.