I do not have any experience of keeping Kune Kunes although I believe they are the least destructive of all the pig breeds, preferring to mainly graze. Any other breed, particularly prick eared breeds like Tamworths, will dig for England and certainly destroy the meadows. Our last lot of weaners were Berkshires and they went crazy in their digging, mining huge craters underneath very mature trees, more than any other pig breed we've kept.
I guess the best option is fence a smaller area within one of the fields just to see how much they rootle the soil up. That will give you an idea of whether letting them have a larger area is practical or not.