I've found that most all of my Gingers will go dorment in the winter and the come back. I'm in a colder area than you are. I would just let it go for a while and not cut it back just yet.

Unless something drastic happened to the rhizome mass (like bugs ate it) it should pop back out soon. I have Costus Barbatus, Costus woodsonii and variegated Costus amazonicus in the ground here in Gainesville that come back every year after freezing to the ground. I have even had a small amount of luck getting COstus osae Red Rose and Costus Emerald Chalice to come back in very protected locations up close to the house.

I'm just north of Orlando and have had the same thing happen in the past. This year we had that hard freeze that knocked many plants back to the ground. Same thing happened a number of years back. My gingers went right down to the ground. I cleaned up the leaves and stalks so they could not harbor pests. The gingers did not recover until the soil had warmed and they began getting regular water. The rhizomes of your plants should be fine since our soil never froze. Just be patient. Your patience should be rewarded with new shoots as the sun and water increase.

Here is a link that might be useful: pegsters page

The above ground parts might also sprout back...don't cut them just yet.

Here's a little secret that I learned from having to compost a lot of costus that I pruned out of the greenhouse almost continuously:
When you trim off spent (still green, unfrozen) stalks, cut them into pieces about 8-10 inches long and throw them onto a compost heap (also do this with frosted stalks! Ambersky is right!) Wait til about May and you will probably have a whole lot of little baby volunteer gingers coming up from those cut pieces in the compost pile.

I've propogated Costus barbarus, spicatus, stenophyllus, red rose, maroon and green chalice, variegated amazonica, Green Mountain, and varzareum this way for several seasons now.