This is the benefit with the deepest literature. A Cochrane review pooled seventeen trials covering 366 participants and found cold-water immersion reduced delayed onset muscle soreness compared with passive rest at 24 hours (SMD −0.55), 48 hours (−0.66), 72 hours (−0.93) and 96 hours (−0.58) (Bleakley et al., 2012).
Read the authors’ own caveats, though. Study quality was low, results were heterogeneous, and the majority of trials did not actively look for adverse events. And when cold water was compared with contrast immersion or plain warm water rather than with doing nothing, the differences disappeared.
The Sports Medicine meta-analysis reached the same shape of conclusion in blunter language: cold-water immersion “can be slightly better than passive recovery” for soreness. Slightly better than doing nothing is a real benefit. It is not the benefit the category is sold on. Our sauna for recovery page covers the heat side of the same question, where the picture is different again.