I'm very familiar with the notion that what I have come to know as 'counteracting', namely turning my upper body against the direction the skis are travelling, so that I am facing the same direction as the ski bases, has the effect of tightening up a carved turn. What I have never really got my head around is why this should be the case. What is the mechanism at work here?
Assuming we are considering a pure carved turn where the ski tail passes through the same point on the snow as the tip.... (Different story if you are referring to pivoting the skis)
The radius of the turn is determined by the edge angle - the angle between the base of the ski and the surface of the snow.
Due to sidecut a ski tipped to a higher edge angle will bend further permitting a tighter turn radius.
If we are to carve the ski (as defined above) we also need to maintain grip. That is, no sliding of the ski across the direction of travel. So to control turn shape we need to grip and manage edge angles.
We control edge angle with a mix of inclination and angulation. Inclination is how much our center of mass (CoM) is inclined to the inside of the turn. The amount of inclination required must balance the centripetal force of the turn and there's basically only one answer for a given turn radius and speed. If our bodies were rigid beams with no ability to bend we would be limited to a set edge angle for any given turn radius/speed if we wanted to stay in lateral balance. However we can bend at various joints (angulation) and we can therefore incline some parts of the body further than other parts - for example by angulating at the hips the legs may be at a larger inclination than the upper body and allow us to have a greater edge angle on the skis and still remain in lateral balance.
But there's a limit to how much extra edge angle can be obtained with angulation. To keep tightening a turn we need to incline more. Which we can do as long as we have grip.
Grip requires that our platform angle is 90 degrees or less. The ski cuts a groove in the snow as it passes through and the base of the ski rests on the wall of that groove. The platform angle is the angle between that wall (the platform), and the balance axis - the line from the CoM to the edge of the ski in the groove. If that angle becomes more than 90 degrees the ski will slip out of the groove.
If we have grip then we can incline more - more edge angle, more bend of the ski, tighter turn radius for the speed we are travelling.
Don't think the CSIA are really into "counter" as terminology these days. Can't recall the term being used since I've been doing their training the past 3 seasons. (Then again I may be a bad listener.) The concept is addressed in the CSIA's Technical Reference #3 "Separation of the upper and lower body allows for angulation to provide grip".