How does supercooled water stay in a liquid state?

Water does not want to change from a liquid to a solid. In order to do that it must have something to freeze to whether that be dust particles or metal or composite airframes. What we refer to as the freezing point is more accurately referred to as the melting point of water. because it will melt at 0 degrees Celsius but it needs something to freeze on.
SUSpilot is absolutely right (he learned it from me
) Water requires a freezing nucleus. Clay dust seems to be the best one. That's why water at very high altitudes doesn't freeze, not much up there except water and a little bit of air. However, when a Cumulus cloud comes along and sucks a bunch of air from the surface of the earth up into the atmosphere in it's updrafts, it provides freezing nuclei to the supercooled water aloft. That's how hail forms.
Atmospheric pressure affects both the boiling and freezing points of any liquid. Since, the atmospheric pressure decreases with increased altitude, the freezing point of water would be decreased. The freezing point of water at 6000 ft would be less than a whole degree difference from that
of the 32 F freezing point of water at sea level. I believe there is an equation to calculate the temperature exactly; however, I don't have it.