It certainly has been the long spell of intense cold that has destroyed the tissue in the stem. Shrubby monocotyledon's (which Cordylines are) don't have normal wood tissue like dicotyledons. Their stems are made of diffuse interwoven bundles of growth tissue and transport tubes for water and minerals separated by starchy material unlike the annually growing rings of dicotyledons that produce true wood. Once damaged by intense cold (ice crystals), it collapses having lost the turgidity that partly kept it upright.

The lower part of the stem often shoots freely from the base so don't remove it yet. Remember, the large rootball will want to replace it's former canopy quite quickly and any new basal shoots will grow much faster than replanting a new one. Leave it until at least the end of June.