Cold water immersion can reduce soreness and help you feel better between efforts on the same day, but routine use immediately after strength training may blunt some of the muscle adaptation you trained for. Use it strategically around competition rather than habitually after every session.
It reliably reduces the perception of soreness and fatigue, and it helps restore performance between repeated efforts within a short window, such as between rounds of a tournament or across a two-a-day competition schedule. For an athlete who has to perform again in a few hours, that is genuinely valuable.
The inflammatory response following resistance training is part of the signal that drives adaptation. Suppressing it consistently with cold immersion appears to reduce gains in muscle size and strength over time. If the purpose of the session was to build muscle, cooling it down immediately afterwards works against that purpose.
Sleep, adequate calories and protein, light movement, and sensible training load management do considerably more for recovery than any cold protocol, and none of them interfere with adaptation.
Typical protocols use roughly 10 to 15 degrees Celsius for 10 to 15 minutes. Colder and longer is not better. Do not use cold immersion alone, and get medical advice first if you have a heart condition, high blood pressure, Raynaud's phenomenon, or any circulatory disorder. Cold shock is a real risk in very cold water.
More on recovery choices is in Recovery Science and Adaptation.