Cold weather is brutal on cars. Oils thicken and take longer to reach engine components and lubricate, metal and rubber hoses become more brittle and more subject to breakage and stress. Batteries lose power.
In the old days, it was common advice to warm up your car before driving off, to give it a chance to get used to the cold. That was necessary for older fuel injection systems but in modern cars, a warm up is no longer a necessity.
However, we do recommend people give their cars a three-minute warmup. This gives oils a chance to become thinner and reach all the way into the engine. Hoses become more flexible and less likely to crack. Letting the car sit and warm up gives this a chance to happen, before putting additional load on the engine, brakes, transmission and drive train through movement.
Plugging into an engine heater also isn't a bad idea, if your car has one.