We generally shut off our unoccupied upstairs (2 BR, 1 Bath) in the winter. In this latest semi-historic cold snap I had a frozen pipe in the upstairs shower. It is reasonably well insulated for a 130 yr old house and didn't take long to thaw. But it would be smart to have an electric device in the upstairs bath that would kick in when the temps get low. But I'd prefer it to kick in at say 35F or 38F rather than 45F (it's 45F up there right now, and I'd be wasting electricity if it came on on days like today when there's no danger of freezing).

Incidentally I have a K1 kerosene Monitor that I installed about 20 years ago that heats the core of the house very efficiently. Also have a propane fireplace in a bedroom that doesn't need electricity that could keep the house somewhat warm if the power was out for an extended period. Have been very happy with that setup.