I'm not sure what you mean by a shinny coat. Shinny is defined as follows on wiki: Shinny (also shinney) is an informal type of hockey played on ice or the street.
I suppose that the best coat for a game of shinny would be something like lambs wool or a woolen fleece of some sort which is warm, breathes, and allows for wetness to wick away from the body. A puppy will have no more problems with wearing such a coat than playing a game of shinny.
I am quite certain that the coat type is not dependent on diet at all.