Most likely yes, and it doesn't sound good. Thousands of Cordylines have been killed this last winter, so you're not alone. You might want to cut it back beyond where its weeping, see if it shoots from the base.

There is a very good chance that it will shoot from the base as Bamboo says so don't remove it straight away. Leave until mid late June and see what happens (apart from cutting back).

I think where I live SE Northumberland must have gotten away lightly this winter as most in the area, indeed all that I have seen are still in good health with no signs whatsoever of any damage. Swings and roundabouts I suppose...