hes using his own code i believe from another tutorial for the skateboard, not sure. but i dont say copy, i say learn the principles and see what they do different then do your own thing.
i understand why it dont turn as there is no physics to tell it there is turning. like a spaceship on no atmosphere in space. add an impulse and no matter what way you face the impulse will continue in the direction it was directed. there is no friction in space (well nearly none) so theres nothing to make the direction of travel change.
This is how impulse works here.
Therefore you need to add physics based detection on your skis and use the engines built in physics system to account for that. whence the vehicle tutorials are most appropriate as they deal with wheels turning, which uses friction. It cant be difficult to implement surely?