Those people do not just suddenly jump into cold river after years of swimming in hot water exclusively. At least in here, people who engage in that activity start in summer and basically continue until winter. Beginners also tend not to do January swimming first year. They skip the coldest months first year taking cold showers at home instead. The theory is that the body needs time to get used to it.
Also, they do not just jump into water out of nothing, they take little exercise before, try to keep their hair not wet in water etc.
Edit: wiki you linked states the same in the health risks chapter: "Winter swimming can be dangerous to people who are not used to swimming in very cold water."
Ice swimming is easier in the coldest months when the water is a lot warmer than the air. Only the most hardcore swimmers do it in April when the air is warmer than the water. Also I have never heard of someone taking cold showers at home to prepare for ice swimming. I would say most just start when there's enough ice to cut a hole in it, without practicing it for months. Source: Finnish.
People here who are into cold water do it every day. It is supposed to be healthy. Cold water swimming on itself is not usually goal for people in here, it is more of a next steps when cold showers do not feel satisfying for them anymore. Most of them keep cold showering every day, but stop going into lake for some months. I do not know when exactly they resume activity, I never cared enough about it.
Also, they do not just jump into water out of nothing, they take little exercise before, try to keep their hair not wet in water etc.
Edit: wiki you linked states the same in the health risks chapter: "Winter swimming can be dangerous to people who are not used to swimming in very cold water."