Abstract: A snow vehicle comprises at least one runner (20, 20'; 54) by way of a ski which is mounted in such a way that it can be tilted and/or steered by means of manual tilting and/or steering members (5) connected actively to actuators (17, 18, 22, 17', 18', 22'; 153) for tilting and/or steering the runner (20, 20'; 54). In order to ensure greater ease, accuracy and reliability of steering, the invention provides that the manual tilting and/or steering member (5) is connected to the runner (20 , 20', 54) tilting and/or steering actuator (17, 18, 22, 17', 18', 22', 153) by means of a transmission system (30, 26, 27, 126, 127, 26', 27', 126', 127'; 60, 61, 60', 65, 66, 67, 67') constructed in such a way as to be mechanically rigid i.e. with little or no play relative to the position of tilting and/or steering. The vehicle may be of the so-called snowmobile kind, or else a vehicle with no means of propulsion and adapted only to descent, similar to a skibob.