a plea for more cool weather sites for migratory travelers

I can see the concern of a dead battery in the morning with the furnace running all night. If you're concerned that it might happen you could always add a second battery even if it's just sitting on the ground connected with jumper cables.
But you then need to charge it back up while on the road to your next destination. For tat depending on the age of your tow vehicle you may need to look into a DC to DC charger.