This spring, I bought little chrysanthemums (mums) of different shapes and colors at a neighborhood market. They have developed very well and now (in autumn) blossom in beautiful colors, e.g. yellow-with-white-margin and purple-with-yellow-center.

How can I go about subdividing these by now mature plants similar to how the person whom I bought the seedlings from presumably did last autumn or this spring? Is there a link or book with good instructions that can be recommended? 

Side question: Is it a good idea to cover the bed (after cutting back mums) with leafs to protect (and perhaps nuture) plants during the Winter season? We typically get about 2 months of snow here.