You need to consider that some walls may contain water pipes. Not having those warmed up sufficiently could lead to a bursted pipe, which could lead to significant damage.

Please consider moisture (=mold) depending on humidity levels where you are. For example if you have one warm room the air will cool on the uninsulated interior walls to the next room, cooler air can not contain the same amount of humidity so this will condensate on (or in!) your walls. This is a good way to grow mold and get all kinds of expensive health issues.

Adding to what others have mentioned, you probably don't use the same type/source of heat for the full house. A typical space heater is resistive heat, which is simply turning electrical energy into heat energy (at 100% efficiency). Your central heat could be a Gas-powered furnace (converting chemical energy to heat energy at ~90% efficiency), heat pump (converting electrical energy to heat at 300+% efficiency), or a few other options.

In my area, gas is much cheaper per joule than electricity. it ends up being the same price to heat the entire place with gas as it would be to heat just a room with an electric space heater. If I were to use a kerosene space heater, or a heat pump, or whatever else, then the numbers would change.

Yes, basic math says it uses less energy to heat a smaller area than a larger one. But that's assuming the same type, cost per unit, and efficiency. This is unlikely unless you have the worst option on both (resistive electric heat)

You may not use the space, but you likely have water lines that can't handle freezing temps, and other electronics/appliances that assume living space (non condensing humidity being important)

Now, setting your thermostat lower and only heating the room you're in? Maybe. Whole house systems are damn efficient, so if you're moving around the house with the heater, that's a no go, but if you hang out in one closed door room, it's an experiment you might want to try.

Expect the bathroom to be colder than you'd like if you've spent the day in your bedroom/office.

Depends on the efficiency of the heater but, as long as the space is enclosed, almost certainly yes.

Keep in mind that your interior walls aren't insulated, so you'll lose some of your heat to other rooms, probably causing higher-than-expected usage. Along with the bursted pipes, which have already been mentioned, I'd be also concerned about interior temperature gradients and condensation, and resultant mold and mildew issues.

Just to add something: water pipes freezing can be made less likely by leaving the water flowing slowly out of a faucet. Moving water does not freeze as easily. While I wouldn't use this as any kind of regular protection, it can help buy you that extra peace of mind when you're probably fine, but still slightly worried about a particular cold snap.

Several years ago, I had a very lucrative, outdoor job over the winter. Between acclimating to the cold and long underwear, I would be roasting in "room temperatures". I lived alone, and was only home weekends and about 6 hours a night.

I turned my thermostat down to 50F, put an oil-filled radiator-style space heater on a timer in my bathroom, and a heated mattress cover on my bed.

Yes, you can save an ass load of money on heating bills.

If you have plumbing in exterior walls, you need to be careful. I had to leave the cabinets under my kitchen sink open to get some heat back to the pipes.

As many people said, it depends on your system. Some highly efficient central heating can have greater than 100% efficiency, so a space heater MIGHT be more expensive than the central heating unit.

Typically a better way to keep the cost lower is to set your home's thermostat to a lower, but still home safe number, like ~55 degrees F (~15 degrees C) and then use a smaller space heater in the room you are using, or just bundle up with hot tea/blankets/sweaters, but allowing your house to get much colder than that might not be good for your appliances, furniture, pipes, etc.

Depending on how much you want to invest, you can upgrade to a mini-split HVAC system and keep each zone of your home at a different temperature based on needs, and it can be far more efficient (and safer) than managing space heaters.

Keep all rooms safely above freezing, +10 Celsius/ +50F and only heat one room warmer. Calculate the power/fuel you would use then and compare to full central heating (it can be different for every location). Generally speaking in many countries running something that heats or cooles rooms with electricity 24/7 will make your power bill skyrocket. Damage to property caused by the cold like burst pipes and other stuff can certainly cost you any savings made and more.

All these people talking about mould and freezing pipes, and so on, and I as an Aussie am deciding I'm totally out of my depth. An observation; We get only a few days of snow in winter every year. Our pipes don't freeze, our houses don't get mould from this. If you aren't in a cold enough to freeze the pipes type place, perhaps do what Aussies do and heat only one room in the house, it's fine.