Whenever you plan to visit an exposed site, such as one of the volcanic cones, wind becomes a hazard, too.
Overnight, temperature in the bush drops quite significantly, even in
summer. In the alpine regions of the Tongariro National Park and elsewhere,
wintry conditions are always a possibility, often at very short notice.
The sun in New Zealand is very intense because the air is very clear. The hole in the ozone layer adds to this in that you will get a sunburn in no time if you're not careful. Fair-skinned people can end up with a sunburn within less than 15 minutes in the sun here. Suntan lotion etc. is available locally - if you're in any way endangered you will need a high SPF one, i.e., 15+ in most cases. A hat is advisable, sunglasses, too.
If you're from north of the equator, remember that New Zealand is in
the southern hemisphere. That means that while the sun still rises in the
east and sets in the west, its midday position is in the north.
Mosquitos (mozzies) are also present but don't carry disease.
Another species that isn't endangered is the possum. It's an import from Australia and NZ's biggest pest. Yes, they do look cute, but please don't feed them - they munch young shoots by the truckload. Their favourite dish is pohutukawa - that's the tree with the strange red flowers you see all over Auckland. In fact, when you're out in the bush, look for bare branches on trees and shrubs - that's often possum damage. They love apple, too, so don't throw the leftovers away where they can get at it.
An invisible but still unwelcome immigrant is the giardia parasite which now resides in quite a number of NZ's streams and lakes, which means that it's often unsafe to drink from them.
The German wasp is widespread in New Zealand, both in cities and out of town. Feel free to kill any number of them, they're a pest, too.
Apart from this there are no dangerous animals in NZ that you are likely
to come across. In particular there are no snakes.
If you intend to stay overnight, a pair of trackpants may help keep your legs warm at night. For huts and backpackers as well as camping, a sleeping bag is highly recommendable. If you don't have one and would like to buy one, we'll be happy to point you in the direction of some good stores - NZ made outdoor equipment is world-renowned for its quality.
Should you intend to venture into alpine regions, take gloves, a scarf, some woollen hat or similar, and warm and windproof clothing - even in January. This includes trips in Tongariro Park and on Mt Egmont.
Don't forget sunscreen, and if you're near wetlands or waterways, particularly in the South Island, do think about some insect repellent.
Finally, take a torch (flashlight). On longer tramps off the beaten
track, take a map and compass, too.