I've heard of people leaving the plants in so that the soil doesn't wash away the rain and leech out key nutrients. I think it just encourages pests to overwinter myself. I cleaned our garden up a month ago. I just chuck the plants into the compost pile.
Same here Rich. We cover our garden after we rip out the plants. I think the straw helps a lot with soil erosion. We get a lot of snow every winter and I think the straw helps the soil once the snow starts melting.