If you folks can tolerate snowboard carving, Ryan Knapton is an ex freestyle pro who started carving piste as a main focus. In the first 25 seconds he slarves turns goofing off like a newbie, and then the talent show starts.He's not on a race board either. Impressive.
The term "steering" seems to be used in more than one way (which is a big reason I'd shy away from using it in a lesson). The definition you've given is surely one that I've often heard. But I maintain that "manually, muscularly, turning the skis"--with a movement that rotates the feet relative to the upper body, separated at the subtalar joints or at some higher point--is impossible. The skis encounter the snow giving resistance to pivoting. The upper body encounters only air, which gives minimal resistance to pivoting. Any rotational body movement creating an upper-lower body separation will result in the upper body rotating relative to the snow, not a rotation of the skis relative to the snow. An engaged ski is not going to be muscled into making a tighter turn than the ski's design and the nature of its engagement with the snow creates.Steering wheels are things we turn with muscular effort.
I've always understood "steering" when applied to skiing to mean the skier is manually, muscularly, turning the skis, either with the upper body or the feet/legs. Steering = rotating, twisting, pivoting the skis.
Playing the iconoclast again, I maintain that the quality brushed turns you're discussing do not feature tails following the same path as tips. Instead, the feature greater grip in the tips than in the tails, with the tips following a clean arc, but the tails slipping out slightly relative to the paths taken by the tips. Hence the wider tracks such turns leave.But I'd also like to have a readily usable term for ski turns that grip at both the tail and the tip through the entire turn, and make round turns based on the bend in the ski, while slipping/skidding over the surface of hard snow. These turns are not arc-to-arc carved turns by the definition in the paragraph above, but they do rely heavily on the ski's self-turning capability.