Er... raw head cabbages, kept in a cool, dry place, keep all winter. They are one of the vegetables easiest to root cellar.*

Leftover cooked cabbage I'd give about a week in the fridge because after a while the compounds that make it smelly-- make it very smelly and unappetizing.

* we run short of fridge space and I'm not sure about storing food in the garage yet, or I'd just store it.