Sorry folks, it's another Cordyline question

If you have a cool place to put it I would, just frost free. Don't water it too much either. In the Spring bring it out and give it a feed after scraping as much of the old compost off as you can and putting fresh compost, it looks as though the old one was quite a big plant .

put loft unsulatoin round the pot forwinter, and POLYSTIREEN underit.

My cordylines sit in an unheated porch throughout the winter. They get watered when I remenber them. They are all doing well. They all originated from one plant like the one in your photo. (I have ten by the way all about 2 feet tall.)
They are all in separate pots; get fed when I am feeding something else, and when the side shoots get to areasonable size I remove them and pot them up. I use them to fill spaces in the garden while I'm waiting for bulbs to go in. I do exactly the same with Yuccas. My original Yucca looks very much like your cordyline but is green.

Thanks for your replies. Wyeboy, I shall definitely bring the pot into my she/greenhouse which I would imagine to be just about frost free but in view of the new sideshoots I shall also protect as you suggest Derek if the weather is very cold. Better to be safe!
Cestvalere, you are obviously keen on Cordylines, have you ever left one like mine to grow multi stemmed which is what I plan to do?