Ice and dispensing area covered with white powder

My ice maker has a white powdery substance all over the ice and as you dispense the ice it gets all over the glass, dispenser, refrigerator door, and even gets on the floor. This happens even if you change out the filter and run the ice maker empty a couple of times. We have well water that has just been tested and is listed as no problems. Does anyone have an idea what is causing this problem?:confused: