I've never heard a good explanation for why gas consumption is higher in cold water, and mine isn't by very much. You could argue that you're probably putting more air in a BC in cold water, since you have more buoyancy loss from your exposure protection to compensate for, but unless you are see-sawing a lot, that really shouldn't be significant. Obviously, if you are shivering, you're in essence exercising, and you will use gas a lot faster -- but you shouldn't be staying in the water until you shiver. And if you swim to stay warm, you'll use gas faster, too. But if you're doing the same amount of physical work, you should have the same gas consumption.
Edited to add: People often refer to the energy being "burned" to stay warm. In fact, the body has no ability to change its metabolic rate acutely like that, which is why we shiver. Shivering is the body's one way to generate more heat; all the other adaptive mechanisms for cold are related to trying to conserve the heat you already have.