Lay down thick towels--the thicker the better--to soak up mud and melted snow. Use old clothes if towels aren't available. Leave them for about 5 minutes, or until saturated. Wring them out in the sink and repeat the process. Wash the towels in hot water afterwards to prevent the growth of mildew. This technique is useful for flat, solid areas such as basements, porches and patios.
Dig small holes in the garden for water generated by the melting snow to run in to. The top layer of soil may be frozen, which allows water to run across its surface and pool elsewhere. By exposing unfrozen areas, the water can be introduced to a porous surface that will soak it up.
Spread generous amounts of sawdust over the melted snow and mud. This will absorb liquid elements and help prevent it spreading. Alternatively, pour hydrated lime or quicklime onto the mud to help dry it out.
Plant a "rain garden" to help absorb melted snow and liquid mud. Rain gardens have loose, absorbent soils in a shallow "ponding" area and contain perennial plants native to a particular region.