Pine needles will work better than sawdust. Raw fresh sawdust is too fine, encourages mold, fungus and other critters that you don't want. If you can find a few Pine trees in the landscape the needles can be had for free. If you do find them, a layer of about 3 inches or so on the soil around the trunk of the tree will do the job your looking for quite nicely indeed. They will insulate yet have enough air circulation to avoid the common problems associated with winter storage.
Boaz, Kentucky US growing zone 6A