I am growing some cotton in Florida my back-yard. I planted then in styrofoam cups with miracle-grow potting soil.
They seem to be growing fine and i recently had one begin to blossom. Since Florida is more of a tropical climate, i think the cotton can grow anywhere there is enough sun and rain. Humidity and heat seem to make it flourish.
Don't be worried to give cotton "too much sun" the little guys love it. Don't treat them like a cute little rose bush. they are low maintenance and only need a daily watering.