Lifting heavy weights stresses your muscles and you get stronger.
Running long distances or short distances intensely stresses your heart and makes your heart stronger.
Doing something you're scared of (public speaking for example) stresses your psyche and makes you stronger.
So sauna and cold plunge both fall into this category of controlled stress that would unsurprisingly have some benefits.
Some of the best athletes of all time use it consistently in their regimen, including LeBron James (40+ and still one of the best players in the NBA).
Even if the cold water was nothing but a sort of pain-endurance test, that's good for your psyche in a similar way doing scary things like public speaking is good for it.
All these things together, I would bet cold plunge is probably good for you. Definitely that it is more likely good for you than bad for you. What do you have to lose? If there's a cold bath around, I'll jump in.