Beginner Gardening: Frost/Freeze Damaged: Plumbago & Cordyline, 2 by SavvyDaze

SavvyDaze wrote:
Living near the coast in SC, I haven't had to deal with winter damaged plants since I moved here in 2006. Our winters have been very mild until this year. After the recent Arctic Blast (temps in the high teens for several hours), a few plants are showing signs of damage and I would like advice on how to take care of them.

Although I covered most of my plants on the nights where freezes were expected, some were still damaged.

1) (Pic 1) One of my Blue Plumbago shrubs had ice on the some of them stems after I uncovered it. I let the ice melt naturally in the sun. Once it was melted, I noticed the outer layer of bark disappeared with the ice and all I saw was green stem. Two week later and the green stem is brown and any remaining brown bark is loose and looks like it is going to fall off. However, there is still a healthy branch or two with green growth. Any advice on how to proceed in care? We are expecting another few nights of near freezing or temps in the high 20's this week.

2) (Pic 2) I have 3 Cordyline 'Red Star'. None of them have developed trunks yet. But as you can see from the picture, the leaves did receive damage during a recent freeze. Since there is no trunk, I can't really cut it back to remove the damaged parts. I know I shouldn't remove any damage until late winter/early spring, and I don't plan to do so, but I am looking for advice on what to do once the time comes. Despite the fact there is no trunk, would I still try and cut it back at ground level? Or would I just remove the most damaged leaves? Or should I do nothing to it at all and just let it shed damaged leaves on its own?

Thanks!