There are multiple factors involved with being able to drive in cold temperatures even with the onset of cold temperatures being fairly sudden 2-3 days notice.
You should be looking at the following major components: Engine, Cabin, and Tires and looking at them separately and then there are additional subsystems and conditions that will make for an interesting conversation on its own so let's begin:
There are 2 important aspects in making sure that your cabin can provide you a comfortable ride:
- Weather stripping - There are kits that are being sold in auto stores and online that will provide better seals for your cabin during winter. Cold temperatures especially on the spectrum on -25 to -40 C tend to make rubber harder and more brittle and thus when you open the doors and closing them you can break those down and make holes in insulation making it more difficult for you to drive when you have to put on thick gloves and hat and shearling or similar to make sure you stay comfortable(sorta).
- Heater - Make sure it works! Cars like older Zaporozhets had to have separate heaters because of the rear mounted engine and that heater (as it turned out) was basically a pilot light fed by gasoline from the tank heating the air that was pushed into the cabin. If this thing went out... Well you get the idea.
- Windows - In addition to making sure that mounting weather stripping is up to par you will have to look whether or not your glass especially on the Windshield is good. I have personally had issues in one of the cars I owned when I had to defog the the windshield it cracked because of the temperature difference between inside and outside. Thankfully it was only a crack running along the bottom so I could still drive but a spiderweb on your windshield could pose a problem. This is usually not a problem for the newer cars with Tempered Glass installed by the manufacturers but it could be a concern for older ones and for cars that had to have any of the glass replaced, which could be done by the outside parties.
There are several subsystems that will need to be looked at for it to function properly so let's try:
The battery is important not just to start the car but also to make sure that your electrical systems run. A shorted out battery will stop your electrical systems from running. In addition to that the colder temperatures slow down the chemical reaction in the battery thus robbing it from power needed to start your car, so if the battery is 3 years or less and your car will only stay in the cold not for an extended period you can safely leave it in the car and you should be OK to start the car after. If not I would suggest removing it and keeping it indoors and reinstalling before you need to use it. Granted of course that you can remove it, some times it's not that easy especially with modern cars that only have electronic keys. So if you have a batter that is 3+ years old it might be a good idea to replace it.
Engine Block and Motor Oil
Motor Oil needs to stay liquid and be able to be pumped into the engine when it starts so Winter viscosity needs to be appropriate. For the longest time in the US it was fairly standard to have cars with 10W-30 grade motor oil and mechanics looked at you funny when you requested 5W or even 0W oil which performs better at lower temperatures and helps to prevent your engine from seizing because oil pump can't put the what became of motor oil at those temperatures into the engine to lubricate the moving parts.
Engine Block also helps to be heated up using Electric Engine Block Heaters when the car is parked since it provides heat to the block keeping fuel, oil, and coolant at temperatures above freezing so that engine can start better. This usually comes as standard or optional equipement on trucks with large diesel engines to keep the fuel from gelling but that's next.
Fuel and Fuel System
There are different precautions that may need to be taken for gasoline vs. diesel fuel. Diesel Fuel because of generally higher viscosity or presence of bio components at lower temperatures tend to gel so there is usually a heater for the fuel tank and fuel lines that is built in to the car. Whether or not it is hooked up to the Engine Block Heater that may come with the car remains to be seen but usually is. Some diesel engines provide Glowplugs to heat up the block somewhat to help with the start.
Gasoline engines for the most part don't have the problems with gelling fuels and freezing which happens around -50C, however, modern gasolines have additives like Ethanol which freeze at higher temperatures, as well as potentially water that may have been mixed in with the gasoline, that actually can clog the fuel pump and fuel line (I know of several manufacturer's recalls, most notably Nissan Altima recently)
The antifreeze in the cooling system depending on the temperature can contain water and freeze in the pipes or radiator or in the water pump (just watched my friend's Porsche blow an engine due to this). So if you have water instead of antifreeze in the system things might get even worse.
If you do happen to have it frozen you will need to either tow the car/truck to the garage to have it thawed or if you are not particularly afraid to use it I have seen Blow Lamp used under the engine and fuel tank to thaw the engine block and fuel lines on the truck sufficiently to get it started.
And Last by not Least:
When it comes to tires you have to take into consideration the fact that you may have snow and more concerning ice on the road. Tires while seem to be an after thought are important. When temperatures drop summer tires which are naturally harder tend to slip and provide worse traction then all season or winter tires and while the primary purpose of the winter tires is to provide better traction on Snow and Ice one can't overestimate their use if the cold spell persist.
And the very last suggestion: if you're renting a car then you might just call the rental company to help you out of a jam, but for the rest of us having an Auto club membership might just come in handy.
So to make a long story short: If you try to bring your desert tuned car to drive on the Dalton, or Dempster you might not fair so well.