In reply to b.e.c.k:
Castle Hill can be pretty good in Winter, depending on the weather, which can be highly variable. If you planned only a few days there, there's no guarantee it would be pleasant climbing. It can be a bit of a heat trap depending on where the wind comes from. Camper van could be cold at times; it's also worth being aware that there is quite a clamping down on freedom camping in areas where it isn't allowed: you can get quite a hefty fine. Just be careful where you pull up for the night. There is a network of decent campsites, the cheapest are DOC ones.
Roads are not often closed, but ones that do that you might want to travel are the Arthurs Pass road, Burkes Pass towards Lake Tekapo, Lindis pass from Omarama towards Queenstown and Wanaka, and the Crown Range between QT and Wanaka (there is a longer alternative.) Again amount of snow is highly variable, I would recommend having snow chains that fit well.