If you plan to do this now, I'd keep them outside until the cold weather encourages the start of dormancy and the leaves begin to drop. Then bring them into some protection for winter. They don't need the light when dormant but do need sufficiently cold but not much below freezing temps (35F is right about ideal). You decide which of your options is best.

You want to keep the temps as constant as possible. Bringing them inside to a significantly warmer location could trigger the emergence from dormancy too early.

Does the shed have access to electricity? Sometimes something as simple as a lit string of Christmas lights can make a big difference. Or bubble wrap around the pots.