A propane tank get cold in the first place as the result of a process called vaporisation, during which liquid propane turns to gas. This happens at the very low temperature of -43.6°F (-42°C), but well above the liquid propane-LPG freezing point of -306.4°F (-188 °C).
Propane (LPG) is stored under pressure, as a liquid, in a propane tank and is also referred to as natural gas liquids – NGL.
It turns back into a gas by 'boiling' into gas vapour.
To boil, the liquid propane draws heat from the steel walls of the propane tank.
This, in turn, makes the tank feel colder than the ambient temperature.
The propane tank gets even colder when you are actually using the gas.
With sufficient humidity and when you are using gas rapidly, condensation or ice can form on the propane tank.
The visible condensation or frost line indicates the level of the liquid gas remaining in the tank.
Source: https://www.elgas.com.au/blog/2084-can-and-does-propane-freeze-does-lpg-freeze