It's New Zealand. Especially in the mountains, be prepared for the weather to do something utterly unexpected. With no warning. Pack a survival blanket and some concentrated food just in case. NZ has no venomous snakes, only one venomous spider: the katipo, a kind of redback which is rare and only found near the coast), but does have deer, unruly dogs and the occasional feral pig. And keas, large intelligent parrot-like birds which will tear up an unwatched backpack and steal your food. They can actually undo laces and buckles.
The most dangerous things I ever encountered in NZ were weather and terrain - mud, rockslides, sudden mountain rainstorms and wind squalls. Otherwise it's an amazingly safe country, and breathtakingly beautiful, especially the mountains and fjords. If you are hiking, watch out for loose and slippery rocks.
Edit: look after your feet, especially if the boots are new. Blisters are no fun!