We had the same low temps here in Lake Charles, LA. All of your gingers can be cut back. There are different thoughts about when though. I usually cut mine back in late Feb. but you could do it anytime now since everything froze.

Steve

I agree with Steve about the anytime after they freeze Sunny florida had 12 nights of below 32 And I mean what a blast. All my gingers tops are also frozen I find it easier to cut them soon after freezing So I can had some extra mulch before Our next cold spell comes. Some of those rhizomes are so close to the surface or even above ground. They all seem fine though.
James Maloy

I leave the dead on to insulate the roots don't touch until spring comes this year its dragging its feet