It's not a person skiing, but I do see your point. The main gear is fixed so the pilot can use them to turn, unless he uses differential braking but he cant because of the skis attached to the gear. Also this isn't a field covered in snow, but a frozen lake with snow on top of it. It also has clumps of snow here and there, and if landing on snow has similar techniques as landing on grass, then the pilot is trying to keep the nose gear from burying into the snow so hes going to put back pressure on the plane, so that most of the weight is on the main gear and plane retains most of the directional control with its nose wheel(if you look at the video at around :57-1:00 you will see that the pilot is putting back pressure on the plane). The pilot will keep the props spinning a little faster than the recommended taxi setting so that the plane will have more speed so that it won't sink.
Ah so the pilot DOES keep the props spinning faster...so the plane won't sink. This comes back to needing fatter skis on it in the first place. Rockered ones. If the pilot had thought to attach those before he left, rather than the ancient GS boards it looks like he's using now, he could simply float effortlessly above the snow, while slashing turns in front of his bro-bras and dissing the honeys, without even having to try. He'd make it look so easy and fun.