I'm pretty sure the reason for extra energy expenditure (leading to fat loss) in the presence of cold is that the body maintains its temperature by making its mitochondria "leaky" using the protein thermogenin in brown adipose tissue (BAT). Basically this decreases the efficiency of turning stored energy into energy that can be used by the body (ATP) - making more heat per calorie used. Babies are born with almost 25% BAT because there are a lot more factors that make them more susceptible to cold than adults. Most BAT in adults is located on the shoulders and the back of the neck, that's why cold showers that focus on those areas are most effective.
So in the short term, exposure to cold increases the body's mobilization of fat stores to create heat leading to weight loss. This is a very resilient strategy to immediate changes. This actually is more suggestive of a warm evolutionary milleiu as opposed to a creature like a whale or seal that has evolved to live in cold and has fat as insulation.