Snowmobile having a continuously variable transmission

A snowmobile comprising:

• a frame;
• a driver seat supported by the frame;
• a left footrest and a right footrest;
• a rear suspension assembly connected to the frame;
• an endless track supported by the rear suspension assembly;
• a motor supported by the frame, the motor being operatively connected to the endless track for propulsion of the snowmobile;
• a drive shaft driven by the motor;
• a driven shaft operatively connected to the endless track;
• and
• a continuously variable transmission (CVT) operatively connecting the drive shaft to the endless track, the CVT comprising:
• a drive pulley mounted to the drive shaft, the drive pulley being operatively connected to the motor via the drive shaft;
• a driven pulley mounted to the driven shaft, the driven shaft operatively connecting the driven pulley to the endless track;
• a belt operatively connecting the drive pulley to the driven pulley;
• and
• a CVT housing having a first lateral side, a second lateral side, and a peripheral wall extending between the first and second lateral sides, the first lateral side, the second lateral side and the peripheral wall defining together an internal volume of the CVT housing, the drive pulley, the driven pulley and the belt being disposed within the internal volume of the CVT housing, the CVT housing defining:
• an air inlet for allowing ambient air into the CVT housing;
• and
• an air outlet for discharging heated air from the CVT housing, the air outlet being positioned to discharge heated air near the left footrest.