Superman IV is a terrible analogy for that... if we were to use Superman IV, then people can breathe in space as well.
thew comic book lists magic an breathing as part of Superman's weaknesses. before the Imperiex war, Mongul actually helped Superman learn how to hold his breath for longer periods of time so that he could stay longer in space to fight. also, right before he had his extreme power surge in the 90's, when he became a walking behemoth unable to control his powers, the very fight before all of it happened has him thinking to himself how he has to go back down for air, but suddenly the oxygen molecules in his blood increased (or something like that- been a long time since i've read that comic book)...
either way, Superman needs oxygen to breathe. Both Superman II and IV do not count mostly because of their storylines do not exist in the mainline DC universe.