If your using your fridge in 12v mode while on the road, you'll have to upgrade your +12v wiring system from your truck-to-camper so that your truck will supply enough energy to power the refridge. Otherwise your battery will be much less than charged when you arrive at your camp site.
Personally, I'd also check the water level in your battery. I'm guessing the capacity of your battery has been compromised due to lack of water.
When we camp, I always leave the truck running until I have the jacks down.
If you have LED lights I would not worry to much about their use - they use very little power. The furnace will use a lot of energy. While it was surely cold outside, we don't know the "duty cycle" of your furnace (IE: how LONG was it on each hour?) however even if the furnace was drawing 4A and ran for 8hrs straight, you'd still have >= ~50% battery capacity left. (considering a type #24 even with de-rating for the cold weather)
Your battery was ether not fully charged when you parked or has limited capacity. (due to not enough water)