I suspect voles have moved into your lawn. Perhaps you live near an open area that was cleared for development last year, and the voles were forced to move, or their population increased suddenly and they are spreading out. If you feed birds, voles use that food through winter. They can do a lot of damage to trees and shrubs if they chew on the bark through winter - many trees and shrubs die because of vole damage.

Now that the snow cover is gone (I hope!), the voles will move to groundcovers or tall grasses for cover. If you don't have much of that, they will probably be prey for some sort of predators as they move towards a new area with some type of protection. In other words, unless you have groundcover in your landscape or a nearby pasture with tall grass, you probably don't need to do anything to control the voles. If you have groundcover, consider removing it or thinning it out so it is less protection and less appealing to the voles.

Look at these online publications for more information about voles: http://extension.usu.edu/files/publications/publication/NR_WD_009.pdf
And http://ag.utah.gov/plantind/sg_vertebrate.pdf

Your primary concern right now may be how to repair the damage to your lawn. Vole runways usually fill in by mid-spring, but I'd advise core aeration to help loosen the compaction they caused. You wouldn't think such tiny little feet could compact the soil, but they did it while the soil was very wet, so the effect of their travel is worse. Here is a link to info about lawn aeration: http://hgic.clemson.edu/factsheets/hgic1200.htm

Note the statement within the publication above regarding timing of aeration: "choose a day when temperatures are mild and soil is moderately moist, which makes the soil easier to penetrate. Avoid aerifying a wet soil, as it is messy and leads to further compaction of the soil as well. If the soil sticks to your shoes or if the core sample you take sticks to your probe, you should wait until it dries out some before starting the job."

Here is a link to the USU publication "Basic turfgrass Care"; it will tell you when and how much to fertilize your lawn. Use the recommendations for "high maintenance lawns" to hasten regrowth. http://extension.usu.edu/files/gardpubs/hg517.pdf