Actual propane does not freeze at 15 degrees. As you get below -30 you may have trouble with propane staying a liquid and no vapor to burn. Sometimes if the main valve on the bottle is opened too fast it will trigger the safety valve to shut. Close for a minute and open s l o w l y.
Water or moisture in the tank will freeze. Or if it gets into the regulator it can freeze. A mix of butane will not vaporize well below 40 but that would be odd up in VT to get any butane mix.
If the regulator is close to ten years or older I would replace it. If you have a choice I recommend Cavagna brand (amazon) Get new pigtails while you are at it.
+1 to test the system with lighting a range burner before you try the furnace.