A snow cutting tooth design and an associated cutter assembly design incorporating such teeth, wherein the tooth is constructed with a unitary body of steel plate welded to the outside surface of a tubular cutter bar, with bevelled edges creating acute snow cutting edges, along with a central notch also having bevelled edges and providing additional cutting edges as well as additional paths for churning and chopping the snow. The teeth are angularly joined along a centerline, dividing the tooth into a leading portion and a trailing portion, the leading portion being welded perpendicular to the centerline of the cutter bar. Some of the teeth have the rearward portion angled to the left side of the tilling machine, while others are angled to the left side, so that the snow is not moved to either side of the cutter assembly.