And then, do they NEED to be in the hen house at night?
Why do you think they NEED to be in the henhouse at night? Do you have specific concerns? I can't address specific concerns if I don't know what they are.
One reason to lock them in the hen house is predators. Usually it is easer to make a coop predator proof than the run. If you have confidence in your run as far as predators it is not an issue. No one else can make that decision for you. Plenty of people on this forum so not lock their chickens in the coop at night. Either the chickens sleep in the run or the pop door is left open.
The other reason is potentially the weather. I don't know what extreme temperatures you will see wherever you are on North Island. I don't think too much heat will be an issue, especially at night. When it is hot a cool breeze feels good. What is the coldest you are likely to see? That is where the question comes in.
I've never been to North Island, but my understanding is that it doesn't get that cold. At least not cold enough for pure cold to be an issue. That would be a long way below freezing. If there is an issue it will be from a cold wind.
The birds that over-winter there (June through August?) have one advantage over your chickens. They can find places to sleep out of the wind if they need to. We can build our coops or runs in a way that they cannot find shelter from a wind. That's where all the concern should be coming from. I don't know if your winters get cold enough for it to be an issue.
Chickens are not as helpless as many think. They can take care of themselves pretty well. The way their feathers lay if they face into a wind and tuck their heads under a wing while sleeping they are streamlined, the wind passes right over them.
I know this is a lot of words without anything that specific. With your run I'd be Ok with them sleeping in there pretty close to freezing. If you are that worried put a wind block on a fence or two, especially if you have a prevalent wind direction. Or train them to sleep inside. Or lock them inside when it is forecast to get really cold.