Hmmm with the fickle weather in NZ it is a bit of a risk to just go with 5 days. Could be 5 days of bluebird weather....... or it may not be.
There will be plenty of snow on Taranaki etc though if you are prepared to risk it..... saw there was a dude from here doing a simmilar thing, perhaps you could track him down.
Ill be hanging round on the south island at that time........ and though it seems like we may have slightly different intentions, if you make it south let me know.