Harvest peppers, eggplants, melons and other warm season crops when the weather gets cold. They are not going to improve in flavor and quality, nor are they going to get any bigger. None are suitable for long-term storage.
Carrots store best if they are left in the ground. Save some bags of leaves and set them over the rows of carrots so that when it snows, you can easily see the rows. (The leaves will insulate the soil and prevent it from freezing.) When you want carrots, simply move the bag of leaves aside and dig the carrots up.