Cold water immersion can affect soreness and some recovery measures, but the result depends on the exercise, timing and outcome you care about.
Systematic reviews report reductions in delayed muscle soreness in some post exercise settings.
Effects vary by the type of performance and the time between immersion and the next effort.
Some research reports temporary reductions in explosive performance soon after cold water immersion.
Immediate cooling may not help every performance measure, so timing deserves more thought when another high power effort is close.
This is one area where the research is more supportive, though effects vary between studies.
Recovery comfort and long term training adaptation are separate questions. Avoid assuming that feeling better means every training outcome improves.