The danger for container-grown plants is that the roots can freeze over winter. There is not much soil to protect them, and a container usually offers little protection. The roots of in-ground plants are insulated by the soil, and even by snow that may fall and cover the plants.
I think you should bring the strawberry jar indoors for the winter. Leave the plants in the container.
If that's not possible, you could wrap the entire jar and its plants very well in several layers of newspaper and burlap, put it up against the wall of your house in the most protected spot you can find. Give it as much protection from the wind as you can. (Then cross your fingers and hope your efforts are successful.
"Isn't it enough to see that a garden is beautiful without having to believe that there are fairies at the bottom of it too?" - Douglas Adams