New Zealand has more alpine mountain terrain than Switzerland, France and Italy combined. In a reasonable season about 10% of New Zealand's total land area is under snow (i.e. approx 30,000 square km). The tiniest fraction of this has ski lifts on it, or ever sees a helicopter land on it. The rest belongs to the backcountry skier.
New Zealand is also characterised by a huge variety of mountain landscapes, from the isolated active volcanoes of the Central North Island, to the glaciated alpine heartland of the central Southern Alps, from the jagged mid-Canterbury ridgelines to the open tops and big skies of the block mountains of Central Otago.
This huge variety of mountains is spaced over a long North-South distance, and affected by weather patterns from all points of the compass, meaning that there is almost always somewhere with good snow, even in what everyone else thinks is a "bad season". A backcountry skier can pick and choose the place and time and always score the goods.
To generalise, most of the terrain is steeper and more rugged than you may be used to. Alpine Touring (AT) gear, or Telemark gear, is used with skins for ascents. Klisters and fishscale bases are limited in their usefulness. There are a few exceptions, such as Central Otago and the McKenzie Basin.