Not really - there are some, but I'd guess well under 1% of the popilation.
For a person who was hardened and used to it, NZ would be fully livable, but it's not a life that many modern people could cope with.
People certianly did that up until about 1880, but they were very different to us.
This is what a relatively wealthy person's house (in a warm climate area) looked like back then, and living out in the bush would have been harsh. This is in probably one of the most livable parts of NZ without power - Thames. And it was also gold mining central at that time.
The house sits on a fully fenced plot, that has a well established kitchen garden along with other trees and shrubs. A water tank to provide much needed 'fresh' water, along with a large chimney to keep the house warm and no doubt for cooking