If I offend with this long reply please forgive me. I think it is important to understand why propane is a poor choice for energy in really cold climates.
First, did you try the hair dryer on the regulator? If it frees with the heat then you have water or oil freezing up in the regulator.
Now for the long winded reply. Propane will boil off at -44F at 1 atmosphere. As pressure in the tank rises it raises the boiling point just as a pressure cooker does to water. When you open the tank to system demand this drops the pressure and the boiling point. Any restriction in the system, say in a regulator will keep the pressure up and you get less boil and consequently less propane gas. The propane boils using heat energy from its surroundings. This cause a cooling effect that can be seen as frost on the tank sides. You will note that the frost is on the lower portion of the tank where the propane is still a liquid. Once the gas enters the piping system it continues to expand in volume as it absorbs ambient heat. When it enters a mixing device such as the venturi pipe on a stove burner it mixes in the proper ratio with air and then "hopefully" is ignited. At really low temperature the amount of propane boiling off may be insufficient to supply system demand. Low, weak flames are the usual indication. Sputtering, yellow flames are a good indicator of propane that is contaminated with water.
We use propane where I work for forklifts, heating mobile command shelters, steam immersion heaters and for helio-torches which are used to ignite oils spills on water. None of the propane tanks have any form of tank heaters. I will check with my certified gas fitter on Monday if he has ever heard of such a a thing.
One last thing. I checked my own copy of the serviceman's handbook and it states that only METHANOL and no other alcohol should be used as an antifreeze in propane tanks. It doesn't say why. Here is a link to the handbook site. http://www.fisherregulators.com/lp/pdf/handbk.pdf