Very interesting and logically supported... just not scientifically supported. There still needs to be studies but the logic i think warrants it. I also believe head shape has something to do with it. Not sure if youve noticed but balding people tend to have wider top of their heads. like wider from the eyes up. i believe this may stretch the skin and compress down down blood vessels (or brown fat) and cause them to atrophy and disappear from the constant pressure. It also makes sense that brown fat would cause hair growth in the sense that brown fat is used as a thermoregulator. You'd expect people who live in colder climates to have more brown fat and more body hair. You'd also expect them to have more brown fat on their scalp and thus more hair on their scalp (following your logic) as this would protect against harsh cold and heat loss from the scalp. Do cold showers actually have evidence to support brown fat production? Ive heard that they have benefits to hairloss but that might have been debunked. If not the two would support each other. More brown fat from cold showers =less hair loss
Well, I know it's a different issue, but people have been using "cold caps" to reduce/prevent hairloss during cancer treatments.