The air taxi pilot initiated flight over an extensive field of glaciers. The passengers described a gray, overcast sky, with a snow field below and snow on the surrounding mountains. They estimated the cruise altitude was between 100 and 500 feet above the glacier. The flight encountered a fog bank in the direction of travel; before reaching the fog, the pilot elected to turn around. During the turn, the airplane descended and collided with the glacier. Postaccident inspection disclosed no evidence of any preexisting mechanical anomaly with the airplane.