This is a very interesting post. When you see a car at the side of the road that has broken down, there is really no telling what happened, and I would say there is no hard and fast rule for what makes cars break down in very cold weather. Just pulling this apart a little more, I would point out that -40 degrees, whether Centigrade or Fahrenheit, is a very, very cold temperature. Most of those reading and responding will never experience it. It's just rare in the lower 48. Secondly, you point out your perception is that it is older cars. Some posters have pointed out that newer cars might be more resistant to this type of breakdown. I agree that frozen coolant, belts, carbs, fuel lines and hoses could be issues. Running out of gas, jammed fuel filters also a concern. Frozen oil even could be a concern.
To prevent this, here are my suggestions:
1. At -40, once the car is started, let it run. Let the heater run. There is a general idea out there that it is better to start driving and let the car warm up normally so as to not waste fuel. That idea is maybe appropriate for the temperate suburbs, but is wanker talk when the thermometer goes so low.
2. In cold weather, the basics are more important. New, properly protective coolant, fresh oil, brake fluid, hoses, belts, tires, leak-free unclogged radiators, new batteries, tested alternators and even spark plugs are your prime locations for failure. Maintenance at low temperatures include gas-line antifreeze, and a topped-off gas tank. And while I love a great thin/thick argument, the deep cold is no place for 20W50 oils.