the first video is how not to do it. the guy is riding like its the last run of the day - or he's just out of shape. he isn't bending his knees! he's riding standing up, stiff legged, throwing his center of gravity from toeside to heel thru his stood up torso
its crap riding. he's falling over and grabbing onto the hill on every third turn...
the second video is how to do it, regardless of the conditions. take it down the fall line, not back and forth all swishy swashy across the whole area... i'm not saying you can't bleed of speed - watch the second video, they turn completely sideways to have total control over speed when they need to - you don't need POW to ride like that. every time they're going perpendicular to the fall line and either stopping or getting that face shot you can do that on fucking ice, you can do that on top of moguls, you can do it in a box with a fox wearing sox.
the key is to do it using your legs, bending your knees, and keeping your upper body centered and quiet. you can lean way over and drag a hand on a huge high-speed pow turn, but you should be centered in an athletic position and moving pretty much down the fall line - even if you do have to sideslip a part or something.