Forget SA!!! SKI NZ! Here Rog, I looked this up for you:
http://www.nzski.com/You will want to: FLY to LA, SF or maybe Hawaii, and then from there fly to Aukland, or maybe Christchuch. Figure 6 hrs across the country and solid 12 hrs to NZ. If you go another direction expect LONGER FLIGHTS...
From either of those cities you COULD FLY to Queenstown which where at least 2 of the 3 locations are on that map. Mt Hutt or whatever I do not recall but the Remarkables come right up out of the glacier fed lake, whereas Coronet I think I back a bit but still you should get some FABULOUS views, spectacular mind blowing views - this is WORTH IT.
The skiing is probably somewhat marginal -- i am just guessing. I have never been there in the Winter, but I don't think its all that great. Those peaks are pretty jaggy and look kinda like the Alps but not nearly so high and i don't think they really get THAT MUCH SNOW...
Still they have vastly MORE SNOW than we have here! :-)
What I would recommend is forget the SKI vacation and make it a multi-week, multi-activity trip.
Fly into the NORTH island AND DRIVE around it, then drive around south island. The terrain, forest and fauna vary greatly -- hit the coast, then the mountains, the jungle and plains... Then one or two days go skiing when it works out, rent some skis...
I'd say go for 3 weeks if you can or longer.
Careful, you may not want to leave...