I think brazil was speaking hypothetically, as in there could be some indirect mechanism, ie
cold water > body’s response 1 > br 2 > … > br N > weight gain.
More specifically, the body does store water. This can create, at the very least, a bloated appearance. Also, as has been pointed out, lowering the core temperature of your body can cause your metabolism to overcompensate.
Or there could just be some really screwed up chemical pathway in the body influenced by excessive cold water. Biology, especially biochemistry, is strange.
For example, cold water might cause a metabolic reaction which diverts more energy towards fat production. Or which triggers cravings to eat more food.
I basically agree, except I would note that our biology is informed heavily by our evolutionary history. It’s easy to see how it might be advantageous to gain fat if exposed to a lot of cold.
Of course, I’m just hypothesizing here. The point is that it’s a potential mistake to model the body as a simple thermodynamic system.
Again, your body does a pretty good job of producing excess heat as it is. So much extra heat that we have special mechanisms (sweating) for shedding it better. Under those high-temperature scenarios, drinking cold water means that the waste heat is just going to be directed inward instead of outward. No extra calories burned, because none are required. I imagine that the only time drinking cold water is really going to burn extra calories is when your body is already on the verge of shivering, and the cold water puts it over the top.
So the people out there that think that all they need to do to lose weight is crank up their thermostat to 85F, put on a heavy coat and sip cold water are in for a disapointment.