seeking advice

Most of the big tramps in the South Island like the Milford and the Routeburn will be under snow and closed. However there are possibilities in the North Island if you don't mind a bush experience rather than a mountain experience. The first one I can suggest in the Lake Waikaremoana walk, which is one of the "Great Walks" and you will find a lot of information about on the net. Other places that have good huts but are less publicised and you are less likely to run into lots of people are the Whirinaki Forest and the Pureora Forest. I have posted information about both on this site. These are all rain forest so you are likely to strike wet, cold conditions but only snow occasionally. But wet snow if you do, which is probably worse! So dress up well. I quite like tramping in the winter here though I tend to make more use of the huts where you can stoke up the fire in the evening and get a bit of social life going. Out there in tents you tend to crawl into the pit at about 6pm so the nights are quite long.

The Abel Tasman or Queen Charlotte walkway are both fine in winter. They are 'coastal walks' so possible to walk for a couple of days then catch a boat to take you back to the car. The main downside is that both tracks are a good 4-5 hours from the nearest international airport. If you want to experience the mountains and are up for a bit of steepness then Lake Angelus & Robert Ridge could be a option. There would be quite a bit of snow in July, the Lake Angelus hut can even be buried. This would also involve a 4 hour drive to Nelson lakes national park from Christchurch airport.

Many thanks for the prompt answers.