Here out west we do most of our camping between November and May. In the coldest parts of winter it will be in the 40s during the day (I know, not that cold) and the 20s overnight. Nobody in my group has ever had pipes freeze because we keep the insides warm enough to not freeze ourselves. I think I'm the oddball in the group because I set the thermostat to 55 overnight while everyone else sets theirs in the high 60s or even 70.
So our experience is that a few hours of cold in the 20s isn't enough to do any damage as long as we keep the inside temps livable.
But Grit's answer is still the most sensible: "Maybe"