Honest question: what makes NZ safer than other countries? I assume it depends on the scenario? Political turmoil could make sense (I don't know enough about NZ politics), global warming probably less so?
While a full on nuclear winter would eventually have global effects, not everywhere would be impacted equally in terms of severity or duration. The most severe effects would be felt in the north. For a more limited exchange with regional or continental wide effects, there are few regions in the north not at risk of such a conflict. With a pattern of impact driven by latitudinal or regional weather patterns, the impact on the southern hemisphere of any regional northern conflict are likely to be minimal.
And easy to (mostly - except for satellite connections) cut off from internet, since there exist only few sea cables to NZ that have to be cut:
They have effectively eradicated COVID, have you seen videos from their elections?