Did knights in medieval Europe wear the colors of their own arms, those of the lord they were serving, or some combination? Was this significantly different in different parts of the continent, or time periods? In peacetime vs when at war?
At the rising of heraldry we could say many of coats of arms were assuming arbitrarily. But after the institution of colleges of heralds(arms), especially in Western Europe, the practice of assuming of arms became more and more regulate during the time. It is obvious that at the beginning there were no laws even in designing(devices) of arms, let alone tincture. Kingdom of Jerusalem's coat of arms (as a early one) is one of the most famous instances of irregularity in canon of tincture: "Argent, a cross potent between four plain crosslets Or."