Cordyline dead?

[BigBundleOfFluff]

Hi, what should I do with this? It wasn't protected during this cold snap we are in, it just about was ok during the December one.
The new growth is brown - I think dead. Should I cut it off or just wait til it maybe grows out a bit?
I won't do anything to until it warms up a bit. It's in a relatively sheltered position by the house but I'm in Scotland and it's Baltic!

I found this thread whilst trying to figure out why my cordyline died. I guess the harsh winter was to much for it. I'll do as @cleowasmycat and @jannier suggested by chopping it down a bit and hoping for the best....