Larry is right, sounds like voles (also known incorecctly called meadow mice or field mice).
Damage to turf can be repaired by reseeding the "highways" they make in the lawn. They can cause severe damage to young trees and shrubs by gnawing on the base of the trunks. This damage can be prevented by removing mulch, ground cover and weeds from the base of plants. Predator odors are most displeasing to voles. Fox and coyote urines can often be bought at trapper supply houses.
The nation that destroys its soil destroys itself.
Franklin D. Roosevelt