As an example, there was a study that eating a handful of almonds every day is correlated with a bunch of positive health outcomes. Then a follow-up paper determined that this is simply because nuts are a relatively expensive snack, so they're eaten regularly mostly by wealthier people. It's well established that being poor is bad for your health, and conversely being rich tends to allow healthy lifestyles in general.
The kind of people that take cold showers are the "health-nut" types that prioritise healthy living over comfort. They're a rare, self-selecting subset of the general population.
It's extremely difficult to do good science based on statistics of self-selecting groups, or groups highly correlated with wealth.
I would probably be characterized as one of the "health-nuts," so between the cold showers, moisturizing twice a day, trying to perfect my indoor air pollution, and literally eating raw spinach and a bowl of fruit for lunch... Who knows what contributes to what?
I probably have health anxiety. I wouldn't characterize it as extreme, but it does force me to do anything I hear is healthy for me.
This applies to pretty much EVERYTHING that is not done via high quality double-blind studies published in reputable, peer-reviewed journals.
Point being: Repeating single actions of successful people statistically does not make you successful.