Later I heard from a doctor that the recommendation was followed by a visible increase of rheumatism, including small children, so they realized it was not that good idea.
Could be a case of post hoc ergo propter hoc. Rheuma has many variants, but generally they are all either autoimmune or degenerative. Juvenile arthritis (JA), an umbrella term used to describe the many autoimmune and inflammatory conditions that can develop in children ages 16 and younger, doesn't include cold as a causal factor.
You can kill cartilage using cold, however I doubt the very cold showers reached the -20°C and below from the study linked. Even then, cold induced cartilage necrosis doesn't necessarily cause degenerative joint disease. It may however cause inflammation? Somewhat dubious, I'd be suprised if so.
Ah, the experiments they did back in the seventies ... unencumbered by ethics boards. Simpler times.
Thus spake Eliezer:
It seems that many here might have outlandish ideas for ways of improving our lives. For instance, a recent post advocated installing really bright lights as a way to boost alertness and productivity. We should not adopt such hacks into our dogma until we're pretty sure they work; however, one way of knowing whether a crazy idea works is to try implementing it, and you may have more ideas than you're planning to implement.
So: please post all such lifehack ideas! Even if you haven't tried them, even if they seem unlikely to work. Post them separately, unless some other way would be more appropriate. If you've tried some idea and it hasn't worked, it would be useful to post that too.