OK, I'll bite.
It seems like the fundamental question that TheRusty is considering is why does higher speeds make turning so much easier in powder. The main physical mechanism involved is "lift", and you don't need to use equations to understand it (at least qualitatively).
By “lift”, I am not referring to conveyances that get you to the top of the mountain or spacers you put between your bindings and your skis, but the force or “lift” that keeps airplanes up in the air. Imagine a ski going through bottomless powder with its tip higher than its tail. The force of the snow hitting the bottom of the ski pushes the ski upwards. This is “lift”. The faster you go (for a given up-angle and snow density), the more lift you generate. Put your hand out a side window of your car at 5 mph versus 30 mph and feel the difference in the wind forces on it. The same thing happens to a 5 mph skier versus a 30 mph skier in powder. Lift doesn’t occur on packed snow – it only occurs when your skis are fully immersed IN snow and can move in all three dimensions, including upwards.
The extra lift generated by going at higher speeds in powder benefits several types of powder turns:
1) If you tend to ski powder smoothly and don't tend to do a lot of unweighting to make turns in deep powder, higher speeds mean that your skis will generally stay in a higher, less dense layer in the snow, so, your skis will be easier to pivot.
2) OTOH, if you make porpoising turns in powder, the extra lift you get from your skis at high speeds means that you will need to rely less on muscular unweighting to get your skis to come up to the surface, or even jump above the surface (where they can be pivoted very easily).
3) Finally, there are powder turns that involve minimal pivoting, banked turns. If you are on a wide open slope, you can make high speed banked turns in deep powder, but you can only do this at fairly high speeds. The physical mechanism behind this type of turn is exactly the same as in a banked turn in an airplane. The lift generated by the tilted wings (or skis) pushes you not just upwards, but also towards the inside of the turn, deflecting the skier (or plane) from a straight path. Go slow, and there is minimal lift and hence minimal force to deflect you from a straight line should you try to bank. Instead, you will just fall over.
This is very different from what happens on groomers. There, you can execute very slow speed RR track turns using just angulation (ie, without any lateral motion of your CM), but these don’t work at low speeds in the 3D environment of deep powder. Imagine trying to angulate/edge at 1 mph in 3 feet of new powder. Your skis will simply descend to the bottom on a sloped path to the side instead of going straight down, but they certainly won’t turn at such low speeds without substantial rotary input.
Finally, (the) Rusty, also asked about a feeling that you can exert “more force” on the snow when going fast, even in a straight line.
On first blush, one would think that this is impossible from the F=ma arguments mentioned above (ie, no centrifugal forces, etc.), but I have a suspicion about what you are talking about. It might be that you are feeling your skis bust through irregularities in the powder/crud that you know you wouldn’t be able to bust through at lower speeds, and hence you realize that you *must be* exerting more force on them at higher speeds to do this. This is absolutely correct. You *are* exerting more force on them. Its just that you are exerting the higher forces for a short period of time at the higher speeds. Its much like a fast moving bullet can go through a wall – it exerts huge forces on the wall, but only for a very short period of time. Am I close to what you are taking about? If not, we can hopefully get some time to chat on Sunday up at WT, but I suspect we’ll have some decent sized crowds to deal with.
Tom / PM