Cut off all leaves, down to the stem, using a sharp knife. Remove damaged or rotten stems.
Cover the stump with straw, and drape a sheet of garden fleece or plastic over the top. Gather and tie the sheet at the base of the trunk, and tie it with string.
Transfer the potted banana tree to a cool place such as a garage floor or frost-free greenhouse, until the weather improves. Once the outdoor temperature reaches 57 to 60 degrees F, it is safe to unwrap the banana tree and return it to its original sunny position.
Trim away all the banana leaves using a sharp knife, cutting back to the base of the stem. If a stem appears brown or is starting to yellow, remove it. Do not leave decaying stems on a wrapped banana tree during cold weather, because mold or rot may develop.
Cut a sheet of garden fleece material or plastic sheeting 12 to 18 inches taller than the banana tree, and wide enough to wrap around the trunk twice. Double-wrapping locks in warmth by trapping air between the the two layers, providing additional protection against weather damage.
Wrap the sheet loosely around the tree to form a cylinder, with a gap of 4 to 5 inches between the material and the tree. Tack the sheet at the top and bottom with clear tape or staples, to keep it in place as you work.
Fill the gap between the tree and material with straw, and pack down lightly until the banana tree and stems are covered. Starting at the bottom, tie string around the cylinder at 6- to 8-inch intervals to secure the sheet.
Twist the excess material at the top of the tree and tie tightly with string.
Unwrap the banana tree after the winter, once the outdoor temperature remains consistently above 57 degrees F.