Winter 'green manure' is any plant that acts as a ground cover and rots into the soil in spring. Buckwheat, any winter ryes, barley, oats and winter wheat are good green manures in our area.
Growing quickly in our warm fall/winter, its leaves act to break up the rain droplets, preventing soil erosion. Roots prevent nutrients from being leached out of the soil. In theory, when the plant dies with frost, the decaying plant both prevents weeds from growing and returns nutrients to the soil.
Winter mulch helps even out soil temperature. It keeps frost from penetrating too deeply, damaging winter vegetables. It blocks the sun's rays from warming the soil rapidly in the spring so weed seeds won't sprout before you are ready to plant your spring veggies.
If we have a mild winter and the plants don't die, just dig them into the soil a few weeks before planting. They'll decompose quickly.