Originally Posted by Daniel_

Close but no cigar.

The white in ice is disolved gasses coming out of solution as the temperature falls.

The ammount of gasses that will be disolved into the water in the first place is a function of hardness (i.e. mineral content), so the white is not the ACTUAL minerals, but is seen more in mineral rich water.

As has been said already, many of the minerals in water are denatured or driven out by boiling (this is called "temporary hardness") leaving only a smaller portion of the total ("permanent hardness"), also boiling drives off some of the disolved gasses. This is why freshly boiled water makes clearer cubes.