I am on a north facing slope. I think it makes the most sense to have the ceiling joists oriented N-S. I believe the maximum span for a SPF x12 joist is about 10 feet, so the N-S dimension of the building will be about 10'. The wall height may end up being 8 foot tall, I am not sure. Depending on the hill you are building into, the "height" of the building could be considerably less than 8 feet. If it is less than 6 feet, it becomes very likely that Bambi could be on your roof, should there be something interesting up there. I have watched moose (Bullwinkle) jump my 5 foot fence, so Bullwinkle could be up there too. Especially since the moose are only around in winter, and then snow, ice, hard wind-packed layers and so on make the concept of fence height ambiguous. Other farmers in the region have had elk attacking their hay, I've never seen elk on the farm. I am going to assume an elk is just a moose with different antlers. So it could be up on the roof too.
I am pretty sure that having an "earthtube" bring air into the building, should be able to supply some degree of heating in winter. How much I am unsure.
People have been known to put barrels of water into root cellars, to act as a heat source. One thing that occurs to me, is a person could have tanks (rectangular parallelpipeds - aka boxes) up against the wall (tall, wide and not deep), which have a fingers coming out the "back". The fingers are attached to a "copper fin" on the inside, which is sized such that if all the water freezes, the copper fin deforms enough to take up the volume change of the water freezing. The other end of the fingers fits into holes in the wall. The idea is that these fingers are in better thermal contact with the outside air, than the inside surface of the wall. If it starts to freeze outside, these fingers will bring the cold to the copper fin, which will start to cool the water and start to freeze it, which will release heat to the inside of the cellar. The question then becomes will the amount of water last long enough to protect the food which is inside?
I was thinking about partitioning the room so that one part could be apples (which I grow here) and the other part could be potatoes. And maybe a person needs a 3rd part for squash? Which has a different T/RH regime than potatoes. Apples and other fruit which emit ethylene gas, need to be stored differently than potatoes. As ethylene basically has the same density as air, you can't rely on it concentrating on the floor or ceiling. So, if you have apples in the same building, they probably need to be stored in an old freezer (just the shell). They can at least be sealed against the release of the ethylene gas outside of the freezer. You want an air inlet on one side and an exhaust on the other side, and you might want a small fan to "stir" the air inside the container.
A flat roof would be the easiest to construct, and the x12 joists leave ample room for insulation, and will allow for under sheathing ventilation as well. You still need to deal with extra water (aka rain, snow, ...) on the roof. You need some overhang, if nothing else to cover the ends of exterior insulation on the walls.
I would put a solar chimney on the south side, about midway, to try and assist with ventilation in winter, and to drive ventilation in summer (which would tend to cool the root cellar)..
But, to have this flat roof on a farm, my thoughts are to put a living roof on the root cellar. You still need to do something about excess water, which is mostly concerned with the edges of the roof. So no soil there, that area is reserved for the water works, insulation and then maybe covered with solar cells to store energy for a few 12V fans inside the root cellar. Maybe a few LED lights to illuminate things when the room is occupied?
The soil is somewhat of an insulator in winter (it is probably dry then, at least here) and is more like a lot of thermal mass in summer. But, a living roof wants there to be less insulation in the ceiling, so that the roots in the soil don't get too cold. Is passive heating going to provide enough heat for this? If you do put a living roof on the root cellar, I think you need to put a fence (people building decks would call them railings) on the edges to keep Bambi and friends off the roof. A deck wants railings that can take a 200 pound load in any direction with a safety factor of 2.5 (so a 500 pound load). A mule deer is heavier than most adult humans (here); moose and elk are way beyond humans. So you probably need to make your fence (sorry, I mean railings) quite a bit more robust than for a deck.
It may be, that part of the floor inside the root cellar needs to be raised up (concrete pad), which would make it drier, possibly partitioned off, and positioned such that the "winter heating air" entered this partition first? Would that constitute conditions amenable for squash? The walls at the ceiling could have a small gap, so that this "warm" air could then spill into the rest of the room, and then we would need to find some way to mix the energy. Perhaps one pumps warm air towards the floor with fans (in tubes), perhaps one paints things inside so that radiative transfer is more effective?
If one is using dimensional lumber, thermal bridging is a concern. So you could put a layer of styrofoam immediately next to the joists on the ceiling, and then cover with something like moisture resistant drywall.