The vast majority of moons are small, with masses far less than Earth, or even Mars.  Because of this, most moons have minimal atmospheres compared to Earth, too thin to breath.  Some larger moons have barely enough air for Martians or Himalayans to breath, but most require respirators, if not full environment suits to survive on.  In fact, most lunar colonies use physical or gravitic domes to maintain breathable environments in and around the settlements.