lp tank and sub zero temp
LP does not freeze, but in very cold weather it will not vaporize. I am having this exact problem right now at a mountaintop communications facility I own in VT. We run off of propane as there are no power lines and the weather has been sub-zero for several days. The person who suggested heating the tank is correct. Believe it or not, what the gas company has told us to do, and we did successfully last year when the same thing happened, is to heat the lines with a propane torch long enough to get the propane to vaporize. Once it gets going it will be fine. It is a safe thing to do, I've been assured.
Good Luck