We were down there in 2022, covered both islands. North island if mostly farm and not much hunting areas. Most likely you will go to the South Island. It will be on the cool side, 45-55 during the day if not cooler. You will also need a visa, doesn’t cost much if I remember right and your civic shot record! Clean your boots as they will inspect them, best to make them look like new if you can, if you have mud on them— no go! We had some hiking trips and one of out group and too much mud, they impounded them. She had to buy new boots. It does rain a lot in the south area, they are soaking rains. They do have red stag farms where they grow them for meat. Those are on the South Island. If I remember anything else I can pm you.
Good luck on your hunt
Smokeploe