Not exactly cold plunges, but there are studies on ice baths and data that exists on this for recovery (with the caveat that most studies of recovery products or modalities are small and often heterogenous or difficult to apply to other situations) shows that not only are ice baths not of benefit for recovery, but they are counterproductive and limit training adaptation. But as with most recovery products, if it gets you to actually take time to recover and you believe it is helpful (the placebo effect is significant with most recovery products, even with the knowledge that it is purely placebo) there may be some personal benefit.