I don't know if you can (suspect yes), but I wonder if also you should put a scrap of plywood or something similar on top your cage to keep the core dry. It's usually the combination of cold and wet that hits these hard.

I wondered about that, too. I don't think it would hurt. Thanks.

Also, my mother said she had good success with these just tying up the leaves in winter to keep the tip from filling with water & freezing.

I dumped more leaves on top today and will find appropriate cover tomorrow. The weather has been playing with us lately, soon gonna freeze for real!

You will be talking about Cordyline australis, this seems to freeze back at about 15 degrees F. or so.