Wanderer,
I am totally rubbish in powder, but the little I know about it is that when you turn you have to move both skis together, with the same weight on both of them. When I tried to turn like normal, in a ski lesson, one ski sank into the snow and I catapulted over the front of my skis and I lay there for a bit wondering if I'd bust a ligament in my knee (fortunately I hadn't).
So now I either turn by very gently pivoting both feet and skis together (for some reason I think of shuffleboard when I'm doing this) and ski with my knees extra bent in that funny duck position (you can see from the chair lift if people are ski-ing in powder because their legs are bent like this), or I jump both feet and skis out of the powder at each turn.
More advanced people manage to carve in powder but so far I have been too frightened to try this. Falling in powder is awful because the few times that it's happened to me the ski that has come off has become buried and even when I've found it I still have a terrible job to get it back on because it keeps sinking back into the snow, so I have to compact the snow around it before I can get it back on.
And if you're not careful, and you have your weight too far back, the front of the skis come up and you accelerate like a rocket, something like planing in a dinghy with the spinnaker up, and you get that nasty feeling where you can't turn or stop.
Oh, and according to the ski instructors, even snow-plough turns don't work in powder
I would much rather ski on ice than powder, but I think I am in the minority of one here. Maybe if there is lots of powder when I get to Meribel on Saturday I will just turn around and go back home ...
Ally
Edit
I am talking about deep powder - say a foot or more. I actually find it easier ski-ing in powder up to about 4 inches deep on the piste, because the powder acts as a brake and generally turns a black run into something more like a red one, or even a blue, and I can ski in the same way I normally do.
Another problem I have is ski-ing powder off piste, because of the rocks. I was in a lesson once, and the instructor hit a hidden rock and fell over (just before I hit another rock and also fell over). It's the only time I have ever seen an instructor fall over during a lesson. Luckily we were both okay.