Proper horticultural fleece would certainly help - double it or even treble thickness round the shoots. I use clothes pegs to fasten it together. Buy it by the metre off the roll at your Garden Centre, which is much better value than in a pack.

It's best to remove it on good days when the temperatures allow it, but put it straight back before dusk.

My lovely plant man was telling me the other day that as far as he knows no one in the West Midlands managed to keep their Cordyline outside over winter. The harsh winter killed them. I am considering moving mine (only purchased a week or so ago) into the conservatory or garage over winter to protect it from the worst of the weather. I have been told these plants aren't hardy in the UK. They have recently been considered more hardy because of the milder winters we've been having.

One thing if you do move the plant into the house/garage/green house etc over winter, its probably a good idea to make sure you harden it off before you put it outside again in spring. Particulaly if its been somewhere warm.

Another tip I've read, if the plant is in a pot wrap a few layers of bubble wrap around the pot to help keep the roots warmer.

If we have another winter like the last one, horticultural fleece isn't going to do the trick, I suspect. Consider building a temporary structure round the plant, boxed in with strong polythene (not touching the leaves), maybe filling the spaces with straw or fleece, and with a lid of some sort which can be removed during milder or wet spells.