I think @LuckyGuy overlooked a couple of things. Or at least overthought them a little.
1) Overworked torque converters and clutches generate considerable heat. Automatics generate enough that they are often plumbed into the radiator… or in the case of many US-made cars, should be. Clutches usually generate negligible heat unless they slip, though that requires a combination of over-worn components, overloading, and driver incompetence.
2) It may have nothing to do with the snow or anything. Electrical issues are good for that, as are dropped cigarettes. I think @kritiper nailed that one.
@filmfann I’ve had to use the cardboard in a couple old Corollas, though only when it was cold enough that the ambient air (even under the hood) was cool enough to make airflow through the radiator actually detrimental. Then again, carbureted engines tend to fare a little worse than fuel injected ones when it gets really cold. Retaining enough heat to prevent the gas from condensing before it gets to the cylinder makes the whole internal combustion thing work a lot better than trying to ignite dry air with barely a trace of gasoline in it.