I can't really comment on the campervan situation, I've spent fairly little time there in the last 5 years, I've never really travelled as such in NZ and I don't drive.
The South Island in winter is pretty cold. You might not think it if you're in Northland (the warmest part of the country) in the summer (and I hear it's been a warm summer by NZ standards). Temperatures will range from -10 to 10. You'll see a lot of snow and rain, and there's a good chance there'll be at least one or two 4-7 day snowstorms across most of the island. But if you're from Canada, I can't imagine it'll be anything you can't deal with. On top of blankets and a heater, if you don't have them, stock up on thermals. And I studied in the very south, and was inseparable from my hot water bottle for four or five months of the year. Do what you think you'd personally do to weather those temperatures in Canada and you should be fine.
In three months, you could probably see most of New Zealand twice.
One thing I will say about places to see and things to do, in case it isn't a no brainer: CHECK PRICES. I get the impression New Zealand can be done for pretty cheap if you're careful, but I've seen prices for tourism that are completely unimaginable. The industry knows you've probably come thousands of kilometres out of your way to be there, so a lot of places charge whatever they want, because if you've come all that way to do it, you'll pay almost anything. It costs 12 euro to see the Colosseum, the Roman Forum and Palatinate Hill. It costs the equivalent of 52 euro to see Hobbiton. Things like bungee jumping in Queenstown, glacier walks on Franz Josef, kayak hire and boat rides in the Milford Sound - I have no idea what they cost, and I wouldn't even like to guess. Basically, research prices, and pick and choose carefully.