Most folks on HN are going to go straight to the physiological benefits, and zip past the psychological ones.
I'm a former Green Beret and combat diver. You know what cold plunges are good for? Practicing will power, and bravery.
It sucks. It's the worst thing ever. But it won't kill you. So you do it for the shock and the pain and the fact that you can safely push yourself to do something you and your body realllllly hates, and you can do it without becoming David Goggins or Jocko or whatever.
Just run a cold bath, dump some ice in, and practice being brave.