I haven't done any research into this, but it seems that with all the benefits that cold plunging provides (Cold plunging mimics stress building antifragility), an overzealous person would do it often.

However, it also seems that too much cold plunging would put your body into a state of fight or flight. Because Chronic stress indicates deeper health issues, I'm curious if too much cold plunging could put your body into a manufactured chronic stress state - too much of a good thing type scenario.