Strawberries in containers will be more susceptible to frost damage than plants in the ground. The main reason for keeping them in containers through the winter is so you can put them in a sheltered spot, such as a coldframe, unheated greenhouse, sheltered courtyard with bubble plastic around the pot, or even in the garage--if you can keep them dormant. If you can't keep them sheltered, it is better to plant them out and mulch them heavily.