Many perennials are better left standing over the winter than cutting them down. There are several reasons for this. In addition to many of the perennials having attractive foliage and/or seed heads, they offer food resources for birds. Many birds find the seeds of perennials particularly tasty. The stems of perennials also offer a place for some birds to hide during the winter.
With some marginally hardy perennials, leaving the stems up for the winter aids in overwintering. The foliage helps to insulate the crowns. Mums seem to benefit a great deal from this practice. Another reason to leave stems stand is that if the perennial is a late riser in the spring, the stems will help to mark the spot and prevent any accidental digging in the area that might harm the underground portions of the plant.