A narrow-profile straddle-type motorized snow vehicle specially configured and adapted for traversing inclined mountain slopes, having a continuously variable transmission (CVT), the primary and secondary pulleys thereof mounted rearwardly of the motor and not on the side of the motor to thereby reduce the width of the vehicle in the critical region between the operator's legs where the engine is located and typically straddled by the operator. A single ski is further provided to utilize the narrow profile of the vehicle in the region of the operator's legs, which in conjunction with the re-configured positioning of the vehicle CVT transmission allows the operator to better lean the vehicle when traversing an inclined slope and be able to simultaneously avoid contact with the up slope and/or snow thereon by protruding legs or transmission components which would otherwise impede passage of the vehicle across an inclined slope.