I live in zone 7B-8A and many gingers will overwinter in the ground here. There are some that are more tropical. But, as far as I know they all need filtered light, and lots of humidity. In your climate I would put the pot in a large saucer filled with pebbles, place a couple of long plant supports (taller than the plant) in the pot and place a clear plastic bag over it, put it in an east window with morning light only, and water when dry. Don't fertilize in the winter. This should create a greenhouse for your plant until you can put it outside, under a tree, in summer. But, if it's happy, they can get very big.
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