Placebo, make-believe and self-dellusion often work, especially for the kind of people looking into a miracle cure, which is what such leaders tend to accrue...

Replace it with pure make-believe of "feeling better" (as opposed to any physiological improvement).

Negative thinking can have a detrimental effect on physical health - usually labelled as stress. It seems completely reasonable that positive thinking could have positive heath benefits (assuming that our base line is somewhere in the middle between positive and negative). We should be investigating the mechanisms and encouraging people to do what has positive results.

Homeopathy sounds like a lot quackery to me, but if it works (via placebo or otherwise) and can improve peoples outcomes in a cost effective manner, then I am all for it.

Sure. But that's neither here nor there, as bathing in ice cold water is not the mechanism - positive thinking is.

The idea that the Hof's regime did it, is what's the dellusion.