Answer: Brown Turkey is considered reliably hardy into USDA winter hardiness zone 7, and you are gardening in zone 6 (based on your zip code). The best thing might be to grow it in a very large container and bring it inside in late fall after freezing weather starts to an unheated garage or similar place where it will be above freezing but cold -- say a maximum of 40 to 45 degrees. That way it can stay dormant until spring (keep the soil just barely damp and do not fertilize in winter) when you would take it back outside to wake up naturally with the season.
Or, you can try to overwinter it outdoors. If you use a heavy winter mulch and are careful not to overfertilize it during the growing season, and it is planted in a sheltered spot with protection from winter winds, it might survive outside. This particular variety can bear a crop even if frozen and winter killed back down to the ground, so you could try it and see.
Here are some suggestions on siting and growing figs you may find helpful. You may need to cut and paste the complete url into your browser to make it work correctly.
Enjoy your fig tree!
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