New Zealands weather predominantly comes from the west. The air that comes from the Tasman Sea is heavily laden with moisture. As the air rises to go over the Southern Alps it looses most of the moisture as rain (air at a higher altitude cannot hold as much water vapour as air at sea level). The process of condensing water into rain is exothermic - produces heat. The resulting air is very dry and warm on the east coast.
Hence, the northwesterly weather results in wet drizzly conditions on the West Coast and hot, dry winds on the East Coast.