But I thought you need to go H5 now for in-ground, and H4 was just for ground contact? Or perhaps that's just for piles?
H5 and stainless are required for structural items like retaining walls. I'm not sure if a fence is required to be up to that standard.
My understanding is that H4 is fine for fence posts, as per http://www.weathertight.org.nz/new-buildings/timber-treatment/