Engine oil (level, colour) remember winter engine idling is hard on the oil
Coolant (level, concentration of antifreeze, condition) depends where you live -45 celcius or -50 F is a good level.
Transmission (fluid level, condition, leaks?) Has it been serviced recently? Is the colour of the fluid nice and red and how does it smell (ie: burned smell?)
Power steering fluid (level, condition) Same as transmission: check smell and colour.
Belts & hose (condition) check for crackes and/or frayed belts. Hoses and clamps, check for cracks and leaks
Battery and battery cables (charge level, condition, corrosion) keep the battery clamps clean
Spark plug wires (loose, damaged?) when was the last tune-up? Vehicles are harder to start in the winter
Air filter- make sure to check with a light, if the light shines through the filter it is OK, clean filter by tapping against a wall
Windshield washer fluid- be sure to install winter washer fluids. (you don’t want a solid block of ice in your washer)
Under the Car
Exhaust system (leaks, damage)——- exhaust fumes can kill !!!!!!
Steering (loose, worn or...