A tread made of rubber-like material for a tire for winter travel having a plurality of blocks of a height H, each block comprising a contact face designed to come into contact with the ground when the tire travels and at least one lateral face, said lateral face being covered by a layer of covering material over at least 50% of the surface thereof, and a leading zone designed to come into contact first with the ground when the tire travels, and said block has an oblique direction of extension (J) such that the leading zone of said block is a leading corner, and a part which is not covered by the covering material, said covering material having a modulus of elasticity which is greater than the modulus of elasticity of the rubber-like material forming the block, said uncovered part extending from the leading corner over at least ⅓ of the height H of the block.