Calla Lilies Damaged by Freezing Weather?

I live in the Deep South and have had Calla lilies for many years that I don't have to dig up in the winter. However, this winter we had several days in a row of freezing weather. I cut back all the damage to the head of the bulb. My questions is: Will the bulbs make new leaves (I already had a lot of green growth) or should I start all over?

Hardiness Zone: 9a

By Debbie from Destrehan, LA