This is a great question to be asking yourself. All plants that are grown in the climate zone they are adapted to do not need protecting in the fall when it frost. This of course only applies to perennials, shrubs, and trees. Trees need the frost to begin their hibernation period in the winter. If the tree is deciduous, then as the sap runs out of the tree, the leaves fall off (if it is a Maple Tree, then you can get maple syrup as the sap runs out…sorta). Shrubs also go dormant during the winter, so they enjoy the cold weather to give them a break from growing.
Perennials, depending on what they are, typically will drop all of their sap to the point that the leaves and the stems will become very brittle and just break off. This is good. These types of plants will give you new growth in the spring from the root.
Annuals, however, if they were spring flowers will kill over very quickly and have no chance of recovery. Just pull them up and throw them away.
Mums will bloom very brilliantly until they get several hard frost on them and then the blooms begin to turn brown and ultimately the whole plants turns brown. If you plant the mum, many times it will come out from the root next spring. I always recommend keeping he dead foliage attached because it gives some protection for the root during the winter. Covering the blooming mums will often protect the blooms and let them have a couple more days of brilliance.
Happy Frost