It won't get cold enough to stop Propane gassing in any bottle, minus 140C odd!
However gas draw off rate can and does freeze the regulator preventing gas getting out
Are you confident it is so low Gary? Most refences, and my memory, give its boiling point as around -42 C .
LINK 1 LINK 2
With the bottle getting well covered with thermally insulating ice, this is not IMO altogether an unobtainable low liquid temperature.
Certainly, any airborne moisture in the regulator's atmospherically vented side, could quickly run into causing several issues.
All said, when it comes to caravanning, I will not be venturing out even with propane, in an ambient any where near not being able to use the heater!