Can my 4 yr old play outside with croup?

Yes and no: Most common cause of croup currently appears to be virus infections. As such you may manage the child as if he or she has bad cold. As a pediatrician I have had many patients who developed bad croup, and brought to emergence room in cool night air, and croup got better, and thus sometimes exposure to cool air seems to work. But, like any viral infection, playing in cold or very hot air is not good.

Depends: Depends on severity of croup. Child should be evaluated by physician for severity of croup.

Yes if mild: If your child is otherwise well and not in distress, and without stride at rest, playing outside should be fine.