The propane will still give off gas below its boiling point - remember that it is liquid in the cylinder at ambient temperature (because of the pressure it is under). This is where vapour pressure comes in. Example: water - leave a puddle of water at room temperature and it will eventually all evaporate even though it doesn’t boil - it’s the same with any volatile liquid. Cooling it down will lower the vapour pressure meaning it will evaporate less readily. The only way to prevent it evaporating completely is to freeze it solid.
Nonetheless, the BP Gas Light bottles suffered with reduced gas pressure due to evaporative cooling when used in high demand applications, because of the thermally insulating properties of the cylinder material.