These trails occurred where snowmelt eroded soil from your lawn. It is important to quickly fill in these waterways and reseed or resod them before more soil erodes. If the trails are an inch or two wide, they are called rills. Fill them with quality topsoil, and sprinkle the soil with grass seed. If the trails are large, they are called gullies. Resodding is the best way to repair gullies, because water flowing through them from spring and summer rains may wash out loose topsoil and grass seed. You may find it beneficial to mulch the seeded areas until the grass becomes established. A thin layer of weed-free straw makes a good mulch for starting grass seed. Another option is hydromulch. This product is usually made of paper fibers and is dyed blue-green. Some garden centers sell it as part of grass repair kits.