Most begonias will not be winter hardy - you will need to lift and store the tubers. The mums should be fine and generally will retain some basal foliage through the winter (similar to shasta daisies). A light leaf mulch should work well, but be careful about holding too much wet material over the crown - it can produce rot. Don't look for flowers in spring. Mums flower according to day length and are late season bloomers.