Picture an open differential. Now add a 90 deg bevel gear box so there is a shaft running straight up from each axle shaft, as well as throu the grear box to the drives. The "new" shafts going straight up are topped with variable speeed pulleys with moveable sheevs. If the sheevs are equal distances apart, and the heavy vee belt between them is parrell on each side (the belt provides constant positraction connecting right and left axles shafts) the snow trac goes straight ahead. But when you turn the steering wheel, a linkage to the variator opens a pulley on one side, and closes the other side the same amount. The axles now are forced to turn at different speeds, one slower and the other faster, thus you turn. This is done with no loss of power due to no steering brakes being engaged.
Hope this helps you,
Kirk