You want to plant garden mums in the spring. That gives them the whole summer to establish a good root system. The foliage will die back in the fall after the first good frost, and at that time, you should cut them back and mulch them heavily.
Fall-planted mums are usually in bloom when purchased, and don't have the energy to devote to growing strong, healthy roots, before they get zapped by the frost. It is common for them not to survive the winter, although a few do.
Although mums are perennials, they stop performing as well after a few years. It's a good idea to start new ones every now and then, using cuttings from your old plants.