Leaves are one of the best ingredients for composting. A combination of chopped leaves and grass clippings break down quickly into a fine mulch. It does not take much room for a compost pile. Adding a little soil and some lawn fertilizer and sprinkling with water if needed will help speed the process.
Turning the compost over with a fork or shovel once a month also helps.
Fertilizing your lawn in the fall helps keep it green all winter. Grass will stay green even after it stops growing. Roots take up nitrogen even after top growth stops. Nitrogen is used to make amino acids which are stored in the plants. Amino acids are used to make earlier green growth next spring even before the soil is warm enough to take up fertilizer.