Hatte die gleiche Frage und habe ebenfalls mal im englischsprachigen Raum gegoogelt. Dort habe ich folgende, mir schlüssige, Erklärung gefunden:

"Ice cubes freeze from the outside, so the center of the cube is the last to freeze. Ice is pure water, only H2O, so as the ice cube freezes, all of the dissolved minerals, like the hardness minerals, get pushed to the center. Near the end of the freezing, there isn't much water left in the center of the cube, so these minerals become very concentrated, and they form the "white stuff" - the technical name is precipitate. The hardness minerals that cause the "white stuff" are not toxic."

Quelle: http://www.filtersfast.com/forums/refrigerator-water-filters/112-sediments-egg-white-look-melted-ice-cubes.html