I am not sure where you live, but I actually did this with some success last year, and will do it again this year. My “winter garden” had onions, garlic, spinach, and 2 varieties of lettuce. We had home grown salad at Christmas, and plenty of salad through the winter and spring. Had to cover the bed a little more as the weather got colder.
Just put in compost in the fall and spring, it is actually good for your soil to have plants rather than be barren. I am going to plant winter wheat in addition to the salad garden. The empty beds are going to get Rye or clover to turn under in the spring.
Thanks for the info. I live in Tn - zone 6 - I have enough plastic to give it a second layer if needs be. So be it - I will erect it in the garden.