We never tried carrots in sand, but my parents would store potatoes and onions (separately) in bushel baskets covered with empty, burlap feed sacks. we had an out building that was sometimes used as a chicken house and that's where the crops were stored. No heat, obviously, but they seemed to do fine. My dad discovered that as long as you didn't bother the onions when they were frozen, they'd keep. Just let them thaw on their own and then get what you needed.
