Aimless, the answer is a lot, on both islands, North and South. The West Coast of the South Island is especially rainy. I wound up riding in the rain while bike touring a fair amount of the time. I was there in all four seasons. Not to say there isn't some really nice weather there, but count on getting rained on part of the time, especially in the mountains.

For heavy rain, I had a Goretex two piece rainsuit, but it was fairly useless. It was an early generation and not all that waterproof. The locals would wear heavy vinyl rain jackets or just heavy wool. I often just wore nylon shorts (surf shorts) and a wool or fleece jacket while hiking.

Fortunately, there are huts for overnighting along the tracks and pretty much every town had a campground where you could rent a tiny cabin cheaply. I had a tent, but the little cabins were great. Some of them were tiny A frames with one or two bunk beds in them, plus a litle table and chair.

I haven't spent much time in the PNW, but from what I have read, here and elsewhere, the weather on much of the South Island, especially the West Coast, is very similar.
Don't get me started, you know how I get.