It's hard to write an entry about weather across the entirety of New Zealand, so please don't expect this to be a detailed analysis of weather patterns for the whole country (that can probably be found here, along with day-to-day forecasts and any other weather information you may need). Instead, I will highlight a few regions that have weather patterns that will greatly impact your trip and also point out some of the extreme hazards that weather creates for travelers.
Some areas of New Zealand seem to have fantastic weather year-round, like the Nelson and Marlborough regions. Others seem to be constantly under a pall of rain--especially the West Coast and Fiordland on the South Island. This weather is a blessing, though, because it has created the astounding landscapes there today; still, the Kiwis like to blame any rainy day on the Australians. This is because all of the hot air that flows off of the arid continent of Oz flows across the Tasman Sea, picking up water vapor as it goes. When it reaches New Zealand, it hits the wall of the Southern Alps and has to rise quickly, causing that vapor to turn into torrents of rain. Many areas of the West Coast and Fiordland receive over 5 meters(!!) of rain per year, which falls on 2 out of every 3 days.
As I've said, the rain has helped to shape these two regions. The West Coast is largely temperate rainforest, which makes the Fox and Franz Josef Glaciers all the more amazing, since they are two of only three glaciers in the world that flow into rainforests. Milford Sound in Fiordland is supposedly even more beautiful in the pouring rain because its sheer walls turn into massive waterfalls. However, the rain can also spoil many well-laid plans. I have had two vastly different vacations in New Zealand in the past three years. The first seemed to be completely covered in fog (after all, New Zealand is the land of the long white cloud) and pouring rain. We planned too little time at Fox Glacier and ended up not getting to do a glacier walk at all because it was raining so hard that it was causing boulders to fall onto the glacier. On this recent trip, I managed to spend over three weeks in Fiordland with only two days of rain (although this summer was a very dry one). So, you never know what to expect in these areas, but I would definitely not be on a tight schedule while you travel through them; otherwise, you'll end up missing activities (or putting yourself in danger!) and going home disappointed.
This volatile weather--and the higher you are/further in the backcountry you are, the more volatile it becomes--can very easily kill if you put yourself in the wrong situation. Often, people set off on day walks thinking that it's sunny, so all they'll need is a shirt, shorts, and a water bottle. This is never a good idea. I saw people on the Tongariro Crossing (on the North Island in Tongariro National Park--another area that has very changeable weather) with this gear that were shivering with cold at the top of Red Crater, where a cloud had descended on us and dropped the temperature by what seemed to be nearly ten degrees. It is always advisable to take wet weather gear (raincoat, rain pants, pack cover and a watertight bag for inside your pack), warm clothing (Kiwis swear by their polypropylene thermals, which are light but very warm), extra water, and plenty of food. I also carried an emergency bivvy bag for wrapping up in if I got stranded/lost.
If the cold, wet, and wind don't get to you when you are unprepared, it is likely that the trail conditions will. Even the best-kept trails deteriorate quickly in adverse weather. Only weeks before I walked the Milford Track, people had to be airlifted over sections of the track that had been completely flooded; I also heard a story from another traveler who had all of his electronics (iPod, camera) ruined after he had to wade through shoulder-deep water on the Milford and didn't have a proper waterproof bag. I got stuck at Welcome Flat Hut on the Copland Track because Shiels Creek, the closest creek to the hut and the only major crossing with no swing bridge, rose to dangerous levels and could have swept me down a mountain face had I tried to cross it. If a river looks dangerous, don't cross it. Either take a flood crossing or wait it out!
Even if you aren't walking in the backcountry, the weather should always be a concern. Nowhere is this more the case than on the Milford Road in winter. The Milford Road, which covers the 120km between Te Anau and Milford Sound, is one of the most fantastic roads I've ever been on. Even though it's windy and I got a bit carsick, I loved it because there was new, glacier-carved scenery around every corner. The road is a tourist attraction in itself, but in winter, it is often closed because the sheer cliff faces that make for such delightful viewing are also a perfect breeding ground for avalanches. This road is carefully monitored and closed if the conditions get too treacherous, but other rural roads may not be so well-kept-up, so conditions should always be checked before travel.