Beekeepers put a super of stores under the brood box (no queen excluder) to ensure that there is enough food in the hive for winter; The bees are in the top part of the hive where it's warmer and without an excluder, they have free access to the stores. If a super is above the brood box (without an excluder), there's a good chance that the queen will be laying in the super come spring. If the super is above the brood box with an excluder, the concern is that the bees will move into the super and leave the queen below, with disasterous consequences.
Generally the nadired super is empty by spring, when it can be removed. It would also help reduce drafts around the nether regions if an open mesh floor is used all winter. If you have a 14 x 12 or commercial brood box, there'll be enough stores for winter if full, so a nadired super isn't required.
A National brood box should be big enough to furnish the colony with stores for winter in most cases. However if a single brood box is over-filled in september, either by good forage or a lot of syrup, the space for the queen to lay will be reduced, when you want winter bees to be produced. Under-filled, and the bees might starve or you are faffing about with fondant in February and March. A super of food in addition to what's in the brood box ensures there's enough stores without having to worry.
(Some bees keep a large brood-nest over winter and could run out of food in a single brood box).
From my experience, a slab of insulation on top of the colony reduces winter fuel consumption. Even an empty super filled with scrunched newspaper will be significant.