In the ski instruction circles that I inhabit, there is an ongoing debate about whether ice is the most challenging surface to ski. I tend to believe that steep ice is the most challenging because it allows no room for error; your movements must be perfect. Another instructor thinks deep powder is harder because of the additional fore-aft balancing challenges which that surface introduces. He has an equally valid argument. The point of all this is that there are two parallel universes happening in ski instruction it seems.
In the one where the OP took a lesson, you apparently learn how to ski ice and you learn how to ski powder, bumps, crud, etc. In my world, which is more affilliated with elite race coaching, you simply learn how to ski, and when your technique has developed sufficiently, skiing ice (or anything else) simply works. Around 7 years ago, I can remember being hopeless on ice and posting some questions on Epic. I got some similar advice, but it didn't really help. Then I began learning how to ski all over again, and every season I got better on ice to the point where it became no different than any other surface. Fundamentally, there is no change to my technique when skiing ice. The only thing I change is that I make certain I establish balance on the outside ski early. As BTS and LF pointed out, this can be done be transferring balance to the little-toe-edge of the inside foot prior to releasing the turn. That's it.
If you have the right technique, you can ski ice on pretty much any equipment. Sharp edges definitely help, but not as much as you might think. What matters more is whether your ski has enough torsional stiffness to allow the edges to bite and whether it is narrow-waisted enough (under 70mm underfoot) to easily tip up on edge. Avoid rockered skis on ice; I've yet to see a full rockered ski that can actually carve on hard snow.
A wide stance is not helpful on ice (or anywhere else for that matter). It prevents effective tipping, disrupts the movements that create fore-aft and dynamic lateral balance and interferes with releasing. With most skiers narrower is better. The only exception is for skiers that are squeezing their thighs together to form a platform. Those skiers must ski with a wide enough (fist width) stance so that they can learn to develop independent foot tipping.
You do not need a wider stance to facilitate recoveries on ice. If you are balanced properly over your outside ski, you should never need to catch yourself. When you are in balance, if the ski breaks loose, you will simply displace laterally with the ski while remaining in balance. This is very common when skiing fresh snow over ice. You will be skiing along bending the ski in the soft snow and you'll hit the ice and scoot sideways. You get down to the bottom of the run and you say something to your friends like, "Man, there were a lot of slick spots up there; I was sliding all over the place" and they give you blank looks because they could not even see it and thought you'd managed to avoid all of the icy patches.
In the world of elite skiing, the idea of a steering angle is nonsense. The first movement is always to edge. We don't practice twisting our skis, ever. If we are leaving pencil-tracks on ice and getting very strong release forces which lift the skis off the snow, there may be times when there is some redirection of the skis (either by accident or by design), but this is never caused by an active twisting of the feet. Rather, it is a result of the tipping movements and it is those movements that are used to control the redirection. Trying to twist flat skis at speed is a recipe for catching your edges and crashing spectacularly. If you want to learn how to ski well, practice moving to new edges without *any* direction change. When you can do that while remaining in balance you will be able to ski anything. Magically, you will also be able to redirect as needed even without having practiced it. But you'll also understand my comment about how rarely that is required outside of a race-course.
In general, but especially when skiing on ice, a distinction needs to be drawn between carving and park and ride. True carved turns involve continuously increasing edge angles and require complete balance at all points in the turn. There are several movements that are required to produce this and the best skiers are in constant motion throughout the turn. Nothing stops until the turn releases. Park and ride, on the other hand, is very static. It involves reaching an angle in the turn (and this could be fairly high) and then simply riding edges waiting for the turn to stop. Speed control is not possible with park and ride except by over finishing turns back up the hill. Park and ride skiing is dangerous and even more so on ice.
When you use carving movements, there is no need to do what most people think of as carving, which is to leave pencil tracks. You can create brushed carved turns (which involve uniform lateral displacement). These work very well on ice and can produce turns with whatever level of speed control you desire. Brushed carved turns are a much better (and safer) alternative to skiing ice than park and ride.
Actively extending into the turn and seeking pressure on the ski so that you can stand against it produces park and ride skiing. Unforutnately, it feels really good so it is easy to get sucked into the trap. One of my friends calls it "Masters Racer Disease," which is unfortunately very apt. If you are standing on your ski, it isn't tipping. As counterintuitive as it may sound, elite skiers manage pressure by continuing to give into it slightly so that they can keep increasing the edge angles of their skis. There is is no point in the turn where they feel like they are standing or pushing against the soles of their feet. The outside leg will be long at the apex of the turn, but it got that way because as the center of mass moved into the turn, it pulled it long. The icing on the cake is the counteracting movement which produced the final bit of extension. If you try to get long by pushing on ice, you'll very likely break your ski loose.
Extending into the turn is to be avoided because it disrupts balance. Contrary to Rick's thread on transitions, elite skiers strive to eliminate any moment of imbalance in transition. If you lose balance in transition, bad things happen. At a minimum, you are a passenger while you are falling into the turn. You don't regain control until there is sufficient pressure against your ski to balance against. Often, you are left with insufficient time to do anything other than park on the edge and ride the turn to completion. Some very athletic skiers are skilled enough that they can overcome being out of balance and still produce good skiiing. OTOH, those skiers would be even better if they didn't allow themselves to get out of balance in the first place. More to the point, the vast majority of us have no hope of successfully skiing that way, so why try?
As an idea of the level of balance I'm talking about, it is possible to stand in a stationary postion with skis parallel to the fall line on a green slope, change to new edges without touching poles to the snow for balance, and actually carve a complete turn. Try it. Without having any forces to balance against, it can only be done if you own a very specific set of movements.and understand how to put them together It is a great test of skiing ability.
Angulation, or counter-balance is very important, but it is only one of the required movements. Tipping, flexion (and *passive* extension), counter-balance, counteracting, fore-aft movements of the feet, and proper pole use are all required. If you are lacking in any one of these, skiing ice with anything other than park and ride will be difficult.
When carving ice, it is important to finish the turn with the tail of the ski carving. Doing that is mostly about finishing the turn with strong counteracting. Balance is moving away from forward at the end of the turn, but it doesn't go to the heel and you don't really have to do anything to make this happen if the ski is slicing. If you are over the heel, you are too far back and out of balance fore-aft-wise. Back of the arch is about as far aft as you would normally want to go. If you finish the turn strongly counteracted (and hold the counteraction while changing edges), the tail of the ski will grip.
The idea of resisting with the outside leg is a dangerous one. You don't want to crumple completely, but you do have to continue to give in so that you can keep tipping. This sensation is very different from what most people do, which is stomp on the ski. The outside leg most definitely should not stay long throughout the turn. It will reach maximum length at the apex and then begin to shorten as flexing and tipping continue. If you don't keep flexing and tipping, you are parking and riding.
The over the shoulder look is fine if you are traversing, but if you are actually skiing, doing that involves rotation that will undo any of the good things you might be doing with your skiing. Very likely, it will result in de-edging of your ski which will reduce or eliminate your grip. In ordinary skiing, there just should be no need to do this. Speed control comes from continous tipping which aggressively tightens the radius, not from trying to carve excessively wide turns back up the hill. If you are on a slalom radius ski, carve slalom turns. If you are on a GS radius ski, carve GS turns. Nothing wider is necessary.
Like I said, I feel like there are parallel universes of ski instruction going on. I read about _Metaphor's experience and my first thought was, "Are we even talking about the same sport?" Hopefully this post illustrates some of the differences in philosophy between run of the mill ski instruction's understanding of skiing and how elite skiers approach skiing. I think many of the people on this site are (like I was) actually in search of developing elite skiing skills. Unfortunately, if you are one of those people, I wouldn't say that you are the target audience for most ski instruction. Buyer beware.
Edited by geoffda - 12/7/14 at 10:08am