The propane is stored in the tank in liquid form. It has to change to a gas to make it to your furnace. That takes heat. It is possible that when it is really cold outside, there is not enough heat to evaporate the liquid to a gas fast enough to keep the furnace running.
When I was there in July, the Ranger at the pay booth told us to park in the RV / Trailer parking, unhitch and drive the toad up. He did not make it sound like it was optional.
The RV / Trailer lot was pretty full. Ironically, there would have been room up at the top, had I tried driving the RV up.