You can go to weather.com and get all kinds of info for any location in the country. Search with the city and state, go to the monthly forecast, and then move to whatever month you want. You will see average highs and lows, and down below that, a chart with average highs/lows, record highs/lows, and average rainfall.
This is the page for Natchez.Given those numbers, I would not bother winterizing. Keep an eye on the forecast. For a few days with lows in the mid/upper-20s, just disconnect the water hose and run off your fresh water tank.
I'm assuming you have a heated underbelly. Make sure the furnace is blowing down there if the temps look lower than mid-20s. It might be a good idea to drain the tanks and close the dump valves, leaving the drain hose empty, so it doesn't freeze.
Your biggest problem may be humidity and condensation. You would likely benefit from a dehumidifier. Just set it up to drain in the tub so you don't have to bother emptying it.