Abstract: A snow vehicle of the saddle-riding type utilizes essentially the same upper structure as a motorcycle but mounts a ski on the front fork for steering and an engine-driven endless belt track assembly for powering the device. The endless belt track assembly is arranged for mounting on a rear arm structure in order to maintain surface contact between the endless belt and the snow and thereby improve the operating efficiency of the vehicle. The arm may be pivotally mounted or integral with a rear fork pivotally mounted to the vehicle. An improved endless belt construction is described in which the belt is strengthened by core members and the driving cogs of particular configuration and disposed at prescribed locations with respect to the propelling lugs in order to maintain surface contact between the belt edge and the snow surface during cornering. Also disclosed are various forms of cover structures for the track assembly that prevent the scattering of snow from the belt onto the rider or vehicle parts.