Failure to remove these plants increases the probability your next garden will have many of the same problems as your previous one. Composting plant stalks and stems, almost always a good idea, needs refinement with respect to diseased plants. Since heat generated during the composting process often does not reach a high enough level to neutralize insect and virus problems, it's a good rule of thumb to keep them away from the compost bin. Planting cover crops and applying manure represent two proactive pre-frost activities organic gardeners traditionally use to help prevent soil erosion and improve on the soil's nutrient content. Each option carries its own cautions.
Cover crops are soil and climate sensitive.
By establishing a root system on the land over the winter, they provide protection against wind and rain generated soil erosion. If plowed under during an appropriate pre-planting time, they also add nutrients to the soil. Applying a manure cover for your garden over the winter improves both soil nutrition and texture. While all manures provide some degree of the three basic plant nutrients, nitrogen, potassium and phosphorus, the exact amount they provide depends on both the animal source and the animal's diet. If given the choice, you'll want to coordinate manure type with your planting plans because nutrient planning is always a plant specific process.