Those are voles, not moles.

Once the snow recedes you may see what you think are mole tunnels in your lawn. Chances are those are not the results of moles. Rather, the damage to your lawn may be the work of voles. Voles are rodents and belong to the same family as rats and mice. They vary in size from 3 to 5 inches from nose to tail and have stouter bodies and shorter tails than mice. Damage from vole 'runways', as pictured, is an un-welcome sight as snow melts in the spring. Turf damage is primarily caused by feeding, in which the voles chew the plants down to the crown (growing point) at ground level. Voles may be active both day and night and love to work under the protective cover of snow. The snow provides protection from predators and allows the voles to cause a lot of lawn damage as they work under cover. When the snow recedes and the turf first becomes visible in the spring, vole damage can appear dramatic, especially when coupled with other issues such as low temperature injury or snow mold. As noted above, however, voles feed only on turf grass shoots and the vital crown tissue and root system are typically not disturbed. Very often, grass plants will re-grow in the damaged areas as the weather warms. Generally, with a little raking and TLC, the damaged areas will heal on their own.