The night before last we spent the night at a KOA in Jonestown, PA, just north of Harrisburg. The temps were in the low teens, but we managed quite nicely in our nearly 20 year old Coachmen 33' motorhome. The furnace kept us at a comfortable 72 deg F, and our water system worked fine, with no problems. Our water and waste bays have 2-1/2" flex ducts fed from the main heating duct, that keep the tanks warm enough not to freeze. We do open the sink cabinet doors at night though, to make sure the pipes don't freeze. We also keep the water heater on at night in those temps. Last night and today we're at Ft Chiswell RV Park near the I-81/I-74 intersection in Virginia where the over night low was 2 deg F. The Coachmen still kept us comfortable, although the furnace did run almost non-stop until the temp warmed up a bit this morning. The only issue this time, was that a short pipe to our accumulator tank froze, causing the pump to cycle every time a faucet was opened. About 10 minutes work with a hair dryer fixed that. Tomorrow we head for St George, SC, and the weather will be warming up considerably.
The likelihood is that you'll be fine in your HR with reasonable precautions such as opening the cabinets.