Depending on the location of the root cellar and the resources you have available stone might be a good alternative to pouring a cement foundation. Like with all buildings if you want them to last a long time, you need to have a appropriate cite with proper drainage, and ventilation. Building a random rubble wall into the side of a hill with a naturally insulated roof might serve your desire to build naturally and economically. Random rubble stone walls are surprisingly simple once you get the basic rules down. Here is an example of a
stone root cellar I am thinking of building a stone passive solar green house into the back of a hill with a root cellar deeper into the hill. I'll let you know how the project goes, I plan on starting this fall and winter. Stone is so easily found in Vermont, all you have to do is dig anywhere. Anyway, good luck with your endeavor.