Freezing is not bad, it is the frost which does the most damage plus the structure of the house offers some protection. I just lay a layer of straw which has not let me down yet. Straw slowly decomposes over winter providing heat, nutrients and moisture. End of winter I work it in, the long fiber helps to loosen up the soil. We never go below -5c maybe wind chill can go down further, the screens provide shelter.
Regards,
Arif.