Hutch -
Up here in the Mountains of WV a lot of old folks would store veggies the way you are talking. Find a high spot in the garden (or make one) so that standing water isn't a problem. Lay down several inches of straw or old hay in a circle (your finished product will look like a Native American burial mound). You can store potatoes, carrots, cabbage, turnips, - most any root vegetable -simply by making them into a mound, cover several inches deep with straw or old hay and then a layer of dirt - again several inches thick. Most of the time the family made two or three of these mounds and apparently they work quiet well. The other alternative is a dark root cellar which was usually a cheaply constructed buiding which uses the hillside as it's back wall.
Just a few things I've seen.