Cheryl, from our experience when the weather turns cold here (Southern CA, zone 10b) our bananas go "dormant". The fruit will remain on the plants and when the weather reaches optimum temperature (which is approximately consistent 80-degree weather day and night) the plants will resume growing and the fruit will begin to grow a bit more and then ripen. We have dwarf musa and Hawaiian bananas. They sometimes take about nine months to nearly a year to ripen for us, depending when they develop their inflo. We harvested one stalk of bananas weighing a little more than 50 lbs from one plant in May this year. Next year we are looking at three more bunches. It is too cold for them to ripen this time of year. Our bananas seem to throw their inflos around April/May and sometimes late June.
In your area, you may need to protect your plants from frost so they won't be harmed. A good layer of mulch will also protect the roots and any new shoots. I have read that hay makes good mulch for them, just don't forget to remove it when the weather warms up so they don't rot.
Hope that gives you some idea of what to expect and how to care for your bananas.
Keep us posted!