I am really not understanding what you want to say. And of course you would have had years without snow in the past, as there are always warmer and colder years in any region, there are always fluctuations. But the average temperature determines whether a year where the snow completely melts off is rather likely or unlikely. So the frequency of the snow-free years is a direct measure of the average temperature in that region of the world.
And snow in NZ doesn't tell anything at all on its own. It might just have been a cold year in that region, it could even be, that climate change would mean a cool down for that region. Climate change is about the temperature increase in the sum over all the world. It doesn't mean that every part of the globe equally warms up. A lot of the local temperatures are determined by geographical features and resulting stable weather influences. Take the gulf stream. That makes Europe much warmer than the equivalent parts of the nothern America. But if that fails due to climate change, temperatures in Europe would considerably go down.
And snow in NZ doesn't tell anything at all on its own. It might just have been a cold year in that region, it could even be, that climate change would mean a cool down for that region. Climate change is about the temperature increase in the sum over all the world. It doesn't mean that every part of the globe equally warms up. A lot of the local temperatures are determined by geographical features and resulting stable weather influences. Take the gulf stream. That makes Europe much warmer than the equivalent parts of the nothern America. But if that fails due to climate change, temperatures in Europe would considerably go down.