Snowmobiles operate on a pair of infinitely adjusting torque/RPM sensing pulleys. The front pulley (or primary/drive clutch) is attached to the crankshaft of the engine. The rear pulley (secondary or driven clutch) is attached to either a jackshaft/chaincase or to the driveline that drives the track. The front pulley drives the rear pulley through a belt. There are no gears or gearcase in the "transmission" system. To develop a snowmobile CVT system to an electric vehicle, the output shaft of the motor will have to match the taper of the primary pulley (clutch), and your final drive would have to adapt to the size of the secondary pulley (clutch).
Both pulleys (clutches) are tapered where the belt rides. The belt rides low in the front clutch and high in the rear clutch. That gives you the greatest gear multiplication and low gear ratio for ease of starting. The front clutch is held open by a spring. The rear is held closed by a spring. As the engine RPM spins the front clutch, flyweights force one side (movable sheave) of the clutch toward the other, emparting force on the side of the belt. The belt initially will slip, but as more RPMS are added, the belt squeezes tighter, making the rear pulley move, which moves the jackshaft or driveshaft. As more RPM are added, the belt moves higher in the front clutch and lower in the rear clutch. At max RPM, the belt will be near the outer edge of the front clutch and almost in the center of the rear clutch, giving highest gear ratio for top speed. Most clutches are designed to run on a 1:1 ratio, but there are a few that actually overdrive.
Clutching on a snowmobile is done to the desired engine RPM. If the engine makes it's power at a certain RPM, that is where the clutching is set. On a 2-stroke, going past the powerband means losing power, sometimes substantially. There are many spring/flyweight combinations to set the RPM so that the engine is operating at the most efficient RPM. When you modify components in the engine, you also have to modify the clutching to accomodate the change in powerband.
A good resource for you to look at would be Olav Aaen's book "Clutch Tuning Handbook". It will give you a lot better understanding on how the CVT system on a snowmobile works, and how you can develop the technology for an electric motor and your intended application.
Good luck, when you get it done, post some pics!
2007 RMK 700, 2008 RMK 600, 1995 AC Prowler 2-up, 1980? AC Cheetah