I'll fall back on my default null hypotheses here.

1. The effect is probably minimal if it exists at all.
2. If there is any effect, it is probably negligible if you are doing the big things right.
3. Your body is smart, and responds to changes in its environment with an eye towards improved survival and fitness. It is not a simple CICO machine.

So suppose we have an overweight person who is trying to lose weight. They hear about cold water exposure, and how being cold burns more calories. So they start running 10 miles every day at 5 am wearing nothing but a t shirt and shorts in the middle of winter. Then they go to starbucks, buy some hfcs with a touch of coffee, and go work at their office job that they hate because capitalism or something. Almost certainly, this person's jounts would start to give out quite quickly, but let's say they hate themselves enough to keep at it all winter. At the end of winter, I would be unsurprised if they gained weight. Sure, they exercised in the cold - but more importantly they were over training, consuming a poor diet, and living an otherwise stressful life. One of the body's best defences against coming hard times is to store calories for future use - by increasing appetite, decreasing subconscious calorie burning, and shunting resources towards fat storage rather than, say, growth and maintenance of muscle, skin, hair, etc.

On the other hand, suppose we have the same individual. They start with the premise that their body is already great, but they would like it to be better, and the way they will achieve this is via having fun and living well. Thus, their fat loss program consists of learning how to ice skate at the town park after work, going snowshoing on the weekends with their local hiking group, adopting a journalling routine before bedtime, and frequently inviting friends over for dinner parties where they make sure the emphasis of the meal is on protein and vegetables. They also open up to friends about how they aren't really motivated in their job, and their network of friends helps them gain the skills and industry contacts necessary to get a job that is more to their liking where they get to do interesting and meaningful work with other people whose company they enjoy. At the end of the winter, I would expect this individual to have lost fat despite exercising in the cold. While fat is good for energy storage and insulation, hiking and ice skating are activities where the body generally benefits from having a lower bodyweight - and warmth can be achieved via increased muscle activation rather than fat insulation. Meanwhile, they were spending a lot of time in beautiful natural environments, interacting with people they liked, eating healthy food, sleeping well, and working towards improving their lives in all aspects. "Things are good and I can expect them to get better" is the antithesis of the doom and gloom stress that will likely drive weight gain. Instead, the body will think "the present is not bad, and the future looks easy - and meanwhile, this extra weight is hindering my ability to move easily. May as well get rid of it."

This is why we find hot people hot. In the past when calories were scarce, a high bodyfat percentage indicated that in the hard times you were living in, this person had access to a lot of calories, and you could expect this trend to continue. These days, life is relatively easy, and storing excess calories is an indication that a person finds life to be hard. A lithe person's body indicates that they have rarely experienced difficulties beyond their abilities, and that they generally live a happy life. This is a good indication of genetic fitness, and hence, they are hot. Same reason why having good skin, healthy hair, a cheerful and outgoing demeanor, and perky tits are hot - they indicate a prolonged state of positive life circumstances which potential mates could generally count on to continue.