How does supercooling work?
Ice crystals are only stable if they have a certain minimum size: one cannot, for instance, have one molecule of ice in a volume of liquid water. The minimum size of an ice crystal decreases with sub-freezing temperature, but just below freezing it is large. (See Bryant and Wolfe, 1999, for a more detailed explanation.) Now the chance that a large number of molecules will spontaneously form themselves into such a crystal is small. Consequently, pure water can be cooled well below zero (sometimes to -40C) before ice forms. When you heat it up, it normally will melt at the equilibrium temperature. Usually water will freeze at only a degree or two below zero. This is because a range of substances act as ice nucleators: they act as surfaces on which an ice crystal can grow. The more efficient the nucleator, and the more of them there are, the easier it is to freeze. Conversely, small volumes of very pure water can be supercooled most easily. By the way, supercooling is a bit like superheat
