The title line says it all. I know um.. empirically that it's ok, but I'd like to hear a confirmation of safety and/or a more extensive empirical experiment.
The tank in question is a BBQ tank measuring about 1 ft in diameter and about 1 1/2 ft in height.
Let me just add car gasoline tanks as a reference for comparison. The lore from folks who own a car they do not drive in winter is to fill the tank in Fall, then to park the car in the garage with the tank full. (The typical garage is not heated, but it absorbs heat from the adjacent structure, and so as an extreme the temperature can get close to freezing—32F/0C.) If the tank is left half-full, water condenses (and so Harper's description makes sense), but it condenses inside the tank. Needless to say, come Spring the engine is not too happy to be fed gasoline contaminated with water.
Will water condense in a similar way inside a propane tank left outside in freezing temperatures (of as low as 15F/-10C, say)?