Can rabbits live outside at night in a hutch that's in a shed and inside during the day?

Sure, rabbits can live outside at night in a hutch in a shed as long as the hutch is secure and insulated to protect them from predators and harsh weather conditions. However, they should have access to fresh air and natural light during the day to maintain their well-being. Just make sure the shed is well-ventilated and the rabbits have enough space to move around comfortably.