Sweet potatoes are sensitive to frost and should be harvested before the first frost occurs. If the vines are already dead, you can still harvest the roots, but they may not be as sweet and flavorful as if they had been harvested earlier in the season. The roots can tolerate a few light frosts, but a hard frost will damage them. If you are unable to harvest the sweet potatoes for several more days, it is best to cover them with a layer of mulch or straw to protect them from the frost.