Yeah, bad idea. First tour should be low miles, safe roads, nice weather. And forget the backpack - miserable!!!
RE: the road - From wikipedia: "The road between Rangipo (10 km south of Turangi) and Waiouru is commonly known as the Desert Road, and is frequently closed by snow during winter."
Are you in NZ already? It sounds like maybe not. If you are in the northern hemisphere, I would respectfully and very strongly suggest you try something here, in summer, with nice weather and long days. If you are in NZ, wait for spring/summer.
If you're just going to be in NZ anyway and looking to tag on a bike tour - I think you should reconsider, respect the conditions that exist rather than trying to mentally force them to work out. Just go tour by car, and go back another time.
There's a great set of books - Pedaller's Paradise - one for each island, if you want to do more research. These have some info about road conditions, grades & services. I found them very useful.