From a mechanical perspective, there are two things that matter: oil temperature and how well combustion happens. Obviously, the car won't be efficient until its optimal working temp' is reached. However, we should be more concerned with lubrication at startup, something the thermal camera cannot show.
Society of Automotive Engineers recommends using 0W oil at -40 degrees Celsius. If you use 30W, anything below -10 is problematic.
Can an engine stop working when it's extremely cold? Yes. If you watch Ice Road Truckers, you'll have noticed that they say engines do freeze up if they're stopped for too long. Likewise, Russians are known to start a fire under their vehicles when the conditions are extreme.
But you don't have to shove a grille under the car. In Canada, many folks have engine block heaters, which constitute a small heating element inserted into the engine block and surrounded by coolant. Even at -40C, the engine will still turn over slowly. However, the battery usually doesn't work when it's that cold and needs a boost.
For the most part, you don't need to let the car idle longer than a minute, right? Well, according to this video, the Subaru 2.0-liter boxer only reached 11 degrees by that time. About seven minutes after that, the coolant is at 58 Celsius. So yeah, you really should be careful with the throttle on a cold day. Or you could just redline it and live life like a boss!