Ice: Personally I always iced after the game however it was normally 10 on 20 off twice throughout college. I find this a coaching and personal choice. We have two pitchers who do not everyone else does. Our pitchers rarely throw more than 1 game a week as starters and usually come back as a reliever which is one of our attempts to protect arms. Cooling the arm after a game seems to be important for recovery. The overwhelming majority of trainers and orthopedics I have had contact with do not consider it a valid study, feeling tests need to be larger in scope when it come to basic recovery.
To what study are you referring? I personally don't know of any actual studies. The idea that icing is detremental to recovery is based on research which shows what happens physically when ice is applied. It reduces swelling by constricting blood flow in the capallaries that service muscles, tendons, and ligaments. This alleviates pain and swelling, but hinders recovery time. Inflammation is the body's attempt to repair damaged muscles and ligaments. Now, if you've done extensive damage like a sprained ankle or broken leg, then alleviating the swelling in order to alleviate the pain and slow the flow of blood - which in drastic cases is much greater than with normal muscle use - is medically beneficial as the need to alleviate the swelling and pain greatly outweighs any small reduction in recovery time associated with icing. However, for normal arm discomfort (soreness) associated with normal pitching activity, ice makes little sense as the discomfort isn't anyhting unbearable and is just a sign that the body is repairing small damage to itself. I used to have my kid use ibuprofin for such pain, but have discontinued due to some research on the dangers of consistent use of NSAIDs. There is an argument for icing that contends that after a certain period of time (around 15-20 minutes) of icing, the blood vessels actually adjust by dilating and then provide more blood flow. However, most icing programs for arms don't advise keeping the ice on for that long, so this benefit, known as the "Hunting effect," never comes into play. In the end, though, I doubt icing delays recovery to any degree that would make me tell a kid that actually believes it helps that he needs to stop.