I am not a big proponent of pitchers icing after an outing unless the arm hurts. I have some pitchers who ice occasionally and others who don't. I have a couple of them who like to use the Game Ready for either their shoulder or elbow after a game or the day after. I pretty much leave it up to the pitchers to do as they please.
Running is another topic that I simply educate kids on why their pitching coach (or whoever tells them to run for 30 minutes) is wrong. If they choose to still do it, then so be it. I won't say it hurts them. But the science does not support the concept. In fact, it may be doing just the opposite. Pitching develops very little lactic acid. Running, on the other hand, develops quite a bit. If more people understood the physiology behind muscle activity, more people would understand that distance running to rid lactic acid was incorrect.