Here is a video on an RC snow vehicle I built.
This is actually based on a design I built over 10 years ago. Back then it was smaller and power by a weak brushed DC motor. This a complete rebuild using heavier materials a stronger brushless motor. A single servo-controlled front ski is used for steering. I tried using a rudder also but it did not seem to help much. I have made front suspension with a spring, and the rear suspension is just the wires that the skis are mounted to that are flexing. The suspension is a key part of the design to improve stability at higher speeds.
The entire thing is built pretty fast, using 12 mm thick plywood that is mostly glued the screwed together. The skis are made out of 4 mm plywood and are painted with a layer of glossy paint on the underside.
There is still a lot of room for improvement. For example, this vehicle is pretty top heavy. This causes it to tip over easily when turning too fast. The torque from the motor can also cause it to tip over while accelerating too fast or turning to the right. It would probably be a good idea to make it wider and a bit lower.
In any case, it was an interesting project to experiment with!
Click on the image below to make it larger. It shows the vehicle in the same configuration as in the video.