Weather conditions in winter

Dear forum members, My name is Jiri van Gijsel and me and my wife are planning to visit New Zealand in August of this year. I'm still in the planning stages of our trip and I’m trying to get an idea of the weather conditions in the winter, especially on the tracks. I'm planning to undertake, as many as possible, one or multiple day tramping trips during our stay. We are going to visit both the North and South Island. But I’m trying to get an idea of how to divide my time between the two islands, in relation to weather conditions. We are experienced hikers, but will not be bringing specialized gear for tramping in the snow. I know the basics; that weather conditions can change rapidly and that the more south and higher you get the more likely you are to encounter snow and ice in the winter. But is it, for instance, not advisable to tramp in Arthur’s pass national park in august? The DOC gives recommendations, but my experience is that in other countries, like America for instance, these recommendations are on the safe side. I hope my question isn’t too general to answer. With kind regards, Jiri van Gijsel