When it comes to Asters, depending on your location there are annuals and perennials. Annual Asters have a 50/50 chance of coming back if planted in the ground. This also applies to all annuals in general. Perennial Asters will come back for many years. Some areas will have hardy perennial Asters that grow wild. Any perennial Aster from a greenhouse or big box store will essentially do the same thing.
But I digress. When it comes to winterizing the perennial Asters, not much effort is needed. Newly planted (first winter) plants will need time to become established and get familiar with their surroundings. But it is always safe to apply your favorite kind of coverings (mulch, shredded leaves, straw/hay) during its first winter to ensure the roots don’t become damaged and stunt the growing in the spring/summer.
They are late bloomers and the last bit of food for both the butterflies and pollinating insects. Keeping the plant up for as long as possible is a must. Even keeping it up during the winter is better. Always for the sugars and nutrients to go back into the roots and aid in a larger growth next season. It may also help wildlife to have a bit of food.