A tread made of rubber material for a snow tire having a tread surface intended to be in contact with a road surface when the tire is being driven on, and provided with a plurality of cuts delimited by walls situated facing one another and forming lateral walls of raised elements of the tread. Each lateral wall intersects the tread surface to form an edge corner. At least one lateral wall of a raised element is formed partially or fully by a cover layer extending from the edge corner associated with this lateral wall, of a material having an elastic modulus higher than that of the rubber material of the tread. The raised element has a depression in its lateral wall, delimited by the cover layer. The raised element moreover has a width W and the depth P of the depression is at least equal to 10% of the width W of the element and less than or equal to 40% of this width W. Finally the volume of the depression is less than 10% of the volume of the raised element.