Cut back freeze-damaged foliage to the ground using anvil pruners. Gingers grow from rhizomes; if the ground is not frozen they will re-sprout in the spring.
Cover the garden bed with a 4- to 6-inch layer of pine bark mulch. Since rhizomes grow at or just below the surface of the soil, mulch protects them from frost damage.
Dig up the rhizomes if the ground freezes in your area. Take them inside and spread them out to thaw. Separate and cut off any frozen or mushy spots. Layer in a bucket with pine bark mulch and keep in a cool place until spring. Monitor and throw out any rhizomes that show signs of rotting.