Cabbage can stay in the garden until you will have temps in the mid teens (although it may split). After harvest, it will generally last about a month in a fridge. Long term storage is either in a refrigerator (use those greenbags and wrap each one in paper towels or newspapers), or in a root cellar or pit full of straw below the frost line.

If you are going to leave it in the ground, to prevent it from splitting you should twist the root stock to slow down growth. We use to keep it in our root cellar and they hold up fairly well, but you have to pick off the outside leaves when you get ready to use as they dry out or start to rot if still moist. You end up with what they use to call "white" cabbage. As long as there is some good left it can be useful.

Thank you so much for the info. This is the first time I have raised it and it likes me. I grew green and purple. I will have to try to store some, we cant eat that much! Wally did you leave it in the garden after the hard freeze?