The snow ski is pivotally attached to a snowmobile in order for it to be pivotable about its longitudinal, steering and transversal axes that intersect each other. The ski has a ski sole from which integrally project first and second elongated front lateral keels and an elongated rear central keel. Moreover, rear ski sole depressions are made in the ski sole, at the vicinity of the rear keel. When the ski is in a straight-line position for allowing the snowmobile to move forward in a straight line, it adopts a flat ground-engaging position in which all three keels rest on the ground surface. When the ski is in a turn-carving position for allowing the snowmobile to move forward while turning in a desired direction, the ski is tilted sidewardly with only the central keel and a selected one of the first and second lateral keels resting on the ground, to carve the ground surface in order for the ski to exhibit a self-steering behavior with enhanced gripping effect. When the ski is in this turn-carving position, the ski sole may be prevented from engaging the ground due to the rear ground clearance of the ski sole, even though the ski may become tilted about its longitudinal, steering and transversal axes.