We and our friends camp in mid-20's weather all winter. Sometimes in the teens. We turn on the heat in our campers and nothing freezes. Not the low-point drains, not the FW supply line and not the outside shower. We have never had anything freeze other than the outside hose, and your idea of unhooking and draining it is correct.
If you have temps in the mid-20's - and no higher - for a week, you may have problems, but it sounds like you're looking at overnight lows. Get some more opinions before you worry too much about your trip.
Your camper will not freeze solid the instant the thermometer hits 32 degrees.
2013 Surveyor SP220
2010 Silverado LT 5.3 V8
The world is a great book, of which those who never stir from home
read only a page. - St. Augustine