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.
The North Island volcanoes, principally Ruapehu, are an area of harsh and changeable weather, and are notorious for the icy and dangerous conditions. In spring they become more inviting, and skiing is possible into summer on the upper slopes for those prepared to make the effort. Not often does one ski on an active volcano.
The Mount Cook and Westland regions are familiar to mountaineers. Here the skiing is actually ski-mountaineering, and mountaineering skills, and equipment, are required to be safe. This is world-class touring, and ranks alongside the Alps of Europe. There are lots of good huts, some run by the Dept of Conservation, some by the New Zealand Alpine Club.
The Central Otago block mountains are inland, and some of the coldest areas of New Zealand. These are areas of big blue skies, freezing cold frosty nights and sparkling snow. Cross-country gear works well here. There are few huts, and tourers need to be self-sufficient. The isolation is magnificent.
The Canterbury ranges are made of sharp and jagged ridgelines with ski basins between. The touring is principally composed of going out to a basin, skinning up a nearby peak or saddle, followed by a ski descent. Multi day trips are possible, but most locals pop out for the day or weekend from Christchurch, only 1 to 2 hours drive away.
Other areas are lower mountains, with rolling tops, that need to be accessed by a walk up a steep track through the bush with skis on the pack. Kiwi ski tourers get used to this kind of start to the day.
There is a guidebook to New Zealand backcountry skiing, available from the New Zealand Alpine Club in Christchurch.