DoC has published its list of locations where Freedom Camping is prohibited under the Freedom Camping Act. http://www.doc.govt.nz/parks-and-recreation/places-to-stay/freedom-camping/prohibited-conservation-areas
It’s mostly a list of carparks and similar areas on the fringes, but note that DoC has also (apparently) listed a blanket freedom camping ban across all of Aoraki Mount Cook National Park, except for approved camping sites.
This seems legally dubious if it’s meant to mean the entire National Park, because the Act only states that DoC can restrict “Freedom Camping”, and section 5 of the Act states that “Freedom Camp means to camp (other than at a camping ground) within 200 m of a motor vehicle accessible area or the mean low-water springs line of any sea or harbour, or on or within 200 m of a formed road or a Great Walks Track…” I’ve flicked a query to DoC to ask for clarification.
The Act as passed into law is viewable at http://legislation.govt.nz/act/public/2011/0061/latest/whole.html?search=ts_act_freedom+camping_noresel&p=1