Standing still in -10C/-20C is pretty uncomfortable, but walking is perfectly fine and you even get hot after a while. So I'm not sure this is true.

it's simple thermodynamics: your body needs to keep its temperature around 37C. It needs energy for this. Heat flows from high temperature (your body) to low temperature (surroundings) via the contact surface (naked skin) or via via (clothing,...) The energy that you lose via heat transfer needs to be compensated. You burn food, fat, tissue,.... (I'm not a biologist, so I can't tell you in what order this happens)

Just try to lower the heating in your house in the winter and run around in a t-shirt iso a pullover.

If you don't believe it, just look up what the diet on a polar expedition looks like.