Hello from NZ. There have been a few questions raised along the thread about how it is being handled here, so I thought I would describe it briefly.
We started social distancing practices before the first case was identified. Then the border controls tightened and soon after the border was closed to all but returning Kiwis. People returning had to guarantee they would self isolate for 14 days. More recently (from last week) they are put in to quarantine in hotel rooms. We locked down at around 100 cases and before any deaths. There were 2 days warning and then it was a very strict lockdown, no schools open, all businesses closed, no take aways, only key workers allowed to work, no travel etc - basically similar to UK now but no stages to it, just straight to full lock down. Only supermarkets open, no bakers, butchers etc, no hardware stores, nothing.
Very clear messages were given from the start. It was explained well, and compliance and support for lockdown has been very high. Each day there is a briefing at 1pm from Jacinda and the chief medical officer where all new cases, deaths and recoveries are described, in detail, including new clusters of cases, how they came to be, and information about where every single person who has it caught it from. All deaths are reported on the same day; there have been 5 so far. The level of information is excellent, but I suppose it's much easier with a small population and much smaller numbers. I think people are admitted to hospital with fewer symptoms as a precaution. New cases have been falling for a week now, and today was 19.
I don't think it's the weather / season that is keeping numbers low (currently mostly warm and dry in upper North Island, much more variable in South Island), but the early action, severe lock down, high levels of testing and contact tracing, and general compliance. I don't know how it will pan out in the future, or whether the goal of total elimination can be achieved. A recent survey found 60% of population ok with longer lockdown if needed, and another 28% unsure.