Renee, it depends on the frost line in your area. In lower Michigan, 40 inches is probably safe. In upper Michigan, 48 is more likely. In Florida, the ground probably never freezes to more than a couple of inches. You should be able to call your county extension service, weather bureau, check in a garden center with a master gardener available for questions. With small, light pieces of wood like you are using, you will probably see some frost action no matter what in many areas of the country.