Overwintering Rosemary?

I have a year old rosemary plant. This plant was a cutting from my school and it spent last winter in the greenhouse at my school, then spent a couple months in it's little container in my sister's room in front of the window (to keep it away from the cats). When it got warm enough, I transplanted it in a hanging basket and hung it out on a hook in the garden. The soil appears to be largely clay and silt based, and stays fairly dry if I don't involve myself with the watering and leave it to the rain. When it was smaller, I brought it under the eave in front of the house if it was going to pour and I hung it in front of the kitchen window if it would get too cold. Now I pretty much leave it outside all the time to stick out the weather. The plant is about six inches high and wide now. I checked on it today. No weeds or anything in its pot and the plant looked healthy, as per usual. However, a few of the needles were brown so I pinched them off. This plant has not been harvested from yet as it is still too small. I live in southeastern Connecticut (not sure what our zone is) The temperature has dipped down to 35 degrees Fahrenheit just this weekend so it will probably be a colder winter. I need to do something with this plant to keep it happy and healthy through this coming winter, and I do not think it will do well in its clay soil in a hanging basket outside as it would likely turn into a rosemary ice cube. Anyone had success or any good ideas on how to keep this plant going?