It depends totally on the reactivity of the metals whether they will react with cold water ,hot water ,steam or will not react at all. More reactive metals like sodium and magnesium can react with simply water to form hydroxide because in solutions their hydroxide are stable (they are strongly basic in nature) , while metals with lower reactivity ( relatively lower reactive than sodium and magnesium) like iron react only with steam to first produce hydroxide which is not thermally stable and hence breaks down into iron oxide and water. So this is not only the physical form of water that is controlling the product formation but it also depends upon the nature of metal too. This will not happen if Iron reacts with cold water it will be producing hydroxide ,first thing it will not react with cold water even if it is possible for Iron to react with cold water it will form iron oxide at the end product as iron hydroxide is not stable.
Thus a metal forms oxide or hydroxide depending on the reactivity of metal,external conditions like temperature, stability of the product etc...