Skiis?

[Soldier]

PoorOjdSpike wrote; "Below are comparison distances moved in one turn at 'Fast' on Paved rd, Dirt rd, Open ground and Frozen river, the distances vary quite a bit, I dunno why"

I think I can be of help there, used to coutry ski a bit in my youth.

The snow on either road is flattend by the vehicular and foot trafic, pretty much dawn to the solid rough surface of the road.
Skis do not slide well at all on such surveces. In fact one ends up walking on the skies more than free sliding forward.
Frozen surface, such as the river in your case is way too slipery in comparison to either fluffy and or compact snow. Not enough friction to keep a man steady on his feet, while rigorously showing one foot over the other, in forward, motion.
Deep snow is actually the best for skis verses foot infantry.