A front fork assembly of a snow bike is disclosed having left and right legs, each having an upper leg portion and a lower leg portion. The left leg upper and lower leg portions are linearly movable relative to each other. A right leg has an upper leg portion and a lower leg portion, the right leg upper and lower leg portions are linearly movable relative to each other. A ski mount has a lower end for coupling to a ski and an upper end for coupling to the left and right leg. A linear force element is coupled to the left and right legs with a first end adjacent the first ends of the forks and seconds ends coupled to the ski, the linear force element has a different linear force characteristic than the left and right legs.