I'm not sure what sort of design you have in mind. Will you be digging a level tunnel and pit into the slope until you're deep
enough to roof it over and bury the roof and tunnel with the excavated earth? That's what my family did up in Eagle back in 1976 or so; we were digging into a sandy prehistoric sand dune in the Yukon River valley. Eventually we had a log chamber covered with thick earth, with two separate heavily insulated doors (with a chamber between them) along the level tunnel back to the outside (which was just a few steps from our front door). Total vestibule length was probably fifteen feet with the earth rising beside it from ankle height to "over our heads" and high enough to set full-height doors into the covered trench.
In our case, we had just enough temperature exchange through the logs and earth that in the summer, the cellar stayed at about 40 degrees; in the coldest parts of the winter, being surrounded by frozen ground with very cold air beyond it, the temp would drop to about 28-30, which would be too cold for our potatoes. Thus for a few months of winter we had to keep a five gallon can of
water on the barrel stove, and swap a hot can for a cold one into the root cellar every 12 hours or so. That kept the temp in the cellar at about 34. (It also cost us the worst injury accident the family ever suffered, when calcification in the metal water can obstructed the vent and the can superheated and then exploded all over my father. Heating volumes of water on a
wood stove has to be done VERY carefully.)
Our property was forested with birch and black spruce, and quite honestly I don't think our geographic facing or amount of insolation was very relevant to the temp in our cellar. It was all about soil temp (which was right about 32, being frozen in winter and mixed lenses of frost and thaw in summer) and thermal mass. My view would be that if the
solar facing of your root cellar matters, you aren't deep enough and you don't have enough thermal mass between your cellar and the elements.
Good luck with your
project!