An older (well, OK, my age) gentleman told me his family just dug a trench, filled it with citron melons and watermelon, covered it with thick straw, then heaped soil on it about two feet high. This was in Oklahoma. They kept over the winter, and were fed to the hogs. Others have stored cabbage this way.
Also, saw some plans for setting a metal garbage can into the ground on an angle (in a well drained area), covering it over with a pile of earth. When you need the stored veggies, just dig through the earth over the lid, and take out what you need. Haven’t tried it yet.
Unfortunately, we do not have a basement. Would be ideal. In the North Country, my parents stored their veggies and apples on shelves in a small concrete block building. Had a light bulb on 24/7 to keep the temp cool but not freezing. Worked well. I think we did put a small electric heater in there overnight when we knew it would be significantly below zero.