Water is a deciding factor. If you can turn off and drain the hot and cold water system, and drain the hot water heating system (if that's the type you have) then the house can go below freezing without the pipes bursting. If you need running water or want to use the heating system sometimes then you have to keep the house well above 0C to keep the pipes from freezing. Look around for other things that might freeze also, like plants, canned goods, stored liquids, etc. If you can let the house go below freezing then you can decide where and when to apply heat and when to do without it. If you can not let it go below freezing then you need some minimum amount of heat to maintain it reliably above 0C, and possibly higher if you think power/heat may only be intermittently available. Maybe you can shut off most of the water system and still have some running water available in a basement if the pipes come into the house below the grounds frost line. It's difficult to live without running water though (toilets, showers, cooking, drinking, washing hands, washing clothes.) If you decide you want to let the house freeze then now would be a good time to dig a latrine/outhouse while the ground is still soft. And think about where you'll get drinking/cooking water from. And ways to get clean without much water. Guides to winter camping might be helpful.

You might be able to isolate some rooms (close and insulate their doors) which makes it easier to just heat the part of the house you use the most (again be sure to drain any water based systems in the closed rooms). At least the bathroom probably needs to remain heated and one common living room (which could also double for sleeping in). The basement may need some heating if some water pipes are kept active (maybe not every day since the earth outside the walls will tend to keep it above 50F, but you'd need to keep a careful eye on it since pipes around the edges can still freeze, maybe add some simple battery powered electronic freeze alarms in critical places close to the walls/pipes). If your basement is finished or livable close off the above ground house and live in the basement. The earth outside the basement walls will help keep it above freezing and perhaps make it easier to keep warm (although the cool earth will also suck heat out of the basement as well, it will trend towards 50F (10C).) Be careful with portable heaters, especially fuel powered ones. Have a carbon monoxide alarm and smoke alarms.

One trick I've seen is filling plastic jugs full of water and spray painting them black and setting them in sunlight inside the house. They absorb heat from the sun during the day and release it at night. Doesn't have a huge effect, but it may help some if you have a lot of them. Also open curtains during sunny days to let heat in, and close them at night to provide insulation. Remember that heat rises, so that might be useful to know (block ceiling vents?, heat a room above by heating a room below?) Stop drafts (but make sure some fresh air gets in). Insulate as best you can. Try to seal the insulation, small gaps can let a lot of cold air in, duct tape may help (but let some fresh air in so you can breath).

Insulate your body with layers of warm clothing, especially the head, hands and feet. Some small USB rechargeable hand heaters might be useful to warm up your hands when you need them to work on something. Sleeping with your head under the covers lets your breath warm you, though it also adds moisture so make sure there is some ventilation (you need to breath also!)

A spot thermometer (thermometer that can read temperatures from a distance using a special sensor) will show you where leaks of hot and cold are. Have the tools you need to shut down and drain your water systems in case heating is completely cut off so you can save your house. If life gets really difficult consider going to a public shelter, or maybe you can share space with friends/neighbors. Two or three families living in one house could greatly reduce heating needs and human bodies create heat also.