Field mice or voles chew a lot of turf under the snow, but the damage often looks worse than it really is. Grass in the affected areas usually recovers without repair by the middle of May. If the crowns have been destroyed, scratch out the dead grass and overseed, making sure the seed makes contact with the soil. Cover lightly with compost or peat moss, and keep the area moist until the seed germinates. There is nothing original in this prescription, and the recovery rate depends more on growing conditions than the method of preparation.
Cutting the grass short in the fall, as you have done, is recommended. Power raking to remove thatch may also make your lawn less attractive to the mice. You might try traps and toxicants to reduce the population.
Additionally, make sure that you remove or modify bird feeders. Vole populations can increase rapidly, especially when bird seed keeps them well fed.
Contact your local Cooperative Extension Service office for more information on mouse and vole control.