I am basing my idea on what it felt like to water ski or skateboard.
I am just now reading a little about skiing, and it tends to promote what I was saying about the body moing in the opposite way of the weight shift:
Learning to turn is as important as stopping because it will (A) put you in control of your direction down the hill and (B) let you steer around other people and pick a path down the hill. To turn to the left, slightly drop your right shoulder toward the tip of your right ski, while increasing the pressure of your right boot on your right ski. Hold that position as you are moving down, and your skis will gently round out a turn to the left.
To turn to the right, gently drop the left shoulder toward the tip of the left ski, increasing the pressure on the left ski and your skis will turn to the right.http://skiing.about.com/od/beginningskiers/ss/snowplow_3.htm