"Being cold" does not have any particular caloric advantage until and unless you are cold enough to shiver. Shivering, as it happens, is a fantastic way to burn calories, and 15 minutes of shivering is equivalent to approximately an hour's worth of exercise.
Indeed. Thanks for the correction. The science, as I understand it, is that just being cold, but not to the point of shivering, will help boost your metabolism if you're performing exercise, while just being cold while idle will burn a basically insignificant amount of calories.
"even mild cold that doesn't cause you to shiver starts to burn through those brown fat stores, jumpstarting your caloric burn rate."
Famously, Inuit team drivers for Arctic expeditions would eat all the butter out of the food supplies first.