It will depend on how cold it is and how many batteries you gave. You do not need AC power to run the diesel burner but both the burner and circulating pumps run on 12 volts. If it's really cold and you are running fairly non-stop it will take a toll on your batteries. With 4 batteries you may or may not have an issue. My coach came with 8 but it also has a residential fridge. Ideally, you'd have an Automatic Generator Start installed so that if the batteries got low, the genset would start up to recharge them.
Mark & Leann Quasius
2016 Cornerstone 45A
2007 Allegro Bus 42QRP (Sold)
2012 Jeep Wrangler Unlimited - Rubicon