Once the potatoes are cooked you do need to refrigerate them. Don’t wrap them in foil to bake, as you want to get the excess water baked out of the potatoes so they are not steamed.  Also, if the potatoes are sealed in foil it is sort of like canning vegetables and can cause a food safety issue called botulism.  When you reheat them it’s fine to wrap them in foil.  Note, the potatoes, when initially baked, need to get up to an internal temp of 185° F before removing them from the, cooling to room temp and then chilling.

Have fun!