I have lived in Alaska for 25 years, but I am in Southcentral so it does not get very cold here, usually winter temperatures at my house no colder than -20 Deg F. I worked in the electric motor and generator industry, mostly for the oil companies. I know about large motors more than small motors, but many factors will be the same.
The problem with electric motors in cold climates is lubrication of the bearings, whether they are sleeve bearings or ball bearings. The windings are not affected in a significant way due to the cold temperature. Brushes on DC motors are fine. There is a temperature coefficient of resistance for copper, but it is not a problem with standard motors. As an example, when you start your car at -20 F, the fan motor (12VDC) may squeal due to the bearing being "dry" as the lubricant is not flowing through the bearing.
A car may have most or all of the types of components you are asking about. A car can be started at -30 F (it may clatter a bit) and everything will work, but it is hard on the engine. The electronic ignition will work and the heater motor and window motors will work, and the stereo. In the cold climates, cars and trucks are typically equipped with engine block heaters so the engine will have adequate lubrication on startup. Some people have heaters on their batteries as well, but that is rare, in my experience. Everything else will work okay.
Regarding electronic components and modules, these should have ratings available documenting the allowable operating temperature range. Manufacturers provide data sheets for sensors which show the allowable operating temperatures and temperature performance curves, where appropriate. You may also be able to talk to engineers at the factory.
Anyway, in general things will work, but you will still need to verify that specific components will operate in the environment you are designing for.
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