A sad (but likely) possibility is that your sponginess is a precursor to rot. Keep a careful eye on it. If you are having rot, and it would be hard to imagine that you don't after a week of freezing weather, your best hope is to regrow by sections. Cut off any rotten parts, save non-rotten parts, and put them in a dry location until April or so. Then pot them up.

If this were my plant, I would consider taking it out of the pot, removing the dirt, and hoping that this will head off rotting. Other than that, I don't think there's much you can do other than keep your plant dry and hope. You'll know one way or the other by spring.