I've wondered about it, too, Kyla. The burned foliage in your photo should recover, I think. At least mine did that I protected subsequent to being frost bitten. I seem to always have a bunch of this growing in various ways because the tiny pieces root and form new plants and colonies easily. Mine has been in containers of various types along with other plants and directly in the ground. Those directly in the ground and in some containers have been left out in winter and just have not survived. However, it takes a while for the plant to be completely knocked out. It obviously has some resistance to cold, just not enough where I've tried it. I have a nice patch this year right next to the garage and so far it looks okay. Some with more exposure looks the same as yours. I'm thinking I may turn an empty pot or two over it and see if that will be enough for it to survive outside.
