You can stick your banana in a plastic garbage sack with some peat moss and stick in a cool basement location until Spring, and plant it then. If you replant it now, make sure the potting soil has very good drainage. You can add sand, perlite, or whatever you like to aerate the soil. The best thing you can do for bananas during the winter is NOT overwater them. My advise would be this... buy a soil moisture meter and use it religiously. Don't water it until the soil is almost totally dry. You can kill a banana plant from overwatering very easily, but RARELY from underwatering. The banana "trunk" and roots store lots of water, so they can go a LONG time without watering. If you overwater, the roots will rot and die.

Ok I will try that. I have lots of bananas and never had that happen before.