ajapale if the centre of the plant is dead/rotten, it's a goner I'm afraid. Growth in palm-like plants comes from the heart, even if outer leaves are ok, the plant will die. If the cordyline has more than one branch, and other hearts have survived, cut down the dead one, the remaining parts of the plant will survive.
As a by the by, frost sensitive plants should be protected in severe cold. Use old blankets or buy specialised plant protectors (this is cheap & looks like a see thro sheet) from the garden centre. If the plant is smallish, bank around with mulch/bark which will retain heat. The natural decomposition of mulch generates heat & protects the plant.