When you're climbing a mountain, the temperature decreases (it gets colder), at least in the first layer of the atmosphere, which is called troposphere. (There are four layers in the atmosphere but there are no mountains tall enough to reach the other 3 layers) and the 3 other layer's temperature changes significantly. So in short, the temperature decreases continuously the higher you reach the mountain.
New Zealand lies on the edge of tectonic plates, this causes one plate to go up and the other to go down. This pushes up the earth creating mountains, geysers, etc
