Apparently there have been no credible scientific reports demonstrating that whole body cryotherapy (WBC) works. Everything so far is just anecdotal evidence; it appears it may just be a placebo effect. I couldn't be bothered reading all of this article but this link should explain more http://www.forbes.com/sites/brucelee/2015/11/23/the-cold-hard-facts-on-cryotherapy/#568b12b11334
Cold helps reduce swelling..That is a known fact. It is now widely regarded that cold also helps the body, including muscles, recover far more quickly than by natural means alone..
No, there's physical effects for sure, it's just interrupting a natural process. If you have damage in your tooth, it will swell (inflame) and your dentist absolutely will never freeze it to heal it, because the body needs to clean the infection. Muscle fibers need to repair naturally after exercise, there's no short cuts to repairing muscle fibers. All this does is help with doms, which as an athlete who needs to play on a Saturday and a Wednesday, it's a godsend piece of kit. Go do 10 sets of bar bell squats at the gym to failure, your legs will be absolutely ****ed on Saturday unless, like conditioned bodybuilders, you let your muscles recover naturally and learn, then the doms get less and less each time.