Is it bad to take a cold shower or jump into cold water right after training to reduce DOMS?
To reduce Delayed Onset Muscle Soreness? Well, you wouldn’t think so but looking at this link from Live Science provides a difference of opinion. True, this article discusses the negative effects of ice baths after resistance & strength training only-but it is reasonable to assume that you are going to need to tread carefully when considering taking post-training anti-inflammatory measures of any kind, either through supplementation, drugs or cryotherapeutic actions, if you want the body to adapt by getting stronger & bigger.
Ice baths and cold showers may be exhilarating and reduce post-training pain, but probably at a cost.
There is the real possibility of interfering with actions of the precursor catabolic processes necessary to stimulate subsequent anabolic, muscle-building processes, processes which depend heavily upon inflammation to initiate.
Unfortunately, it looks as if no free lunches are being provided here. Most probably you are going to be required to pay with some pain and inflammation dues to avoid singing those hypertrophy blues.