Well, I suspect it should be Ball Hut and is a backcountry Department of Conservation hut which trampers can stay in overnight whilst out tramping in the backblocks of rural New Zealand.
Hundreds of such huts dot the back end of beyond in NZ.
Some are accessible by 4x4, but only a minimal number would be accessible in this way.
As for Ball Hut, apparently it is "Perched on the edge of the Tasman Glacier moraine wall. Although this hut is only about 5km from the summit of Aoraki / Mount Cook, the summit is hidden from view. Good views of the Tasman Glacier and Malte Brun Range opposite."
However, the most pertinent piece of information for you is that access is "Along old Ball Hut Road (foot access only) from Blue Lakes car park, Aoraki / Mount Cook National Park."
Note foot access only, but that there was once a Ball Hut Road.
Personally, I'd suspect it to be highly unlikely that such a hut would ever have been accessible by road.
Here's a picture of the hut today:
Ball Hut: Aoraki/Mount Cook area backcountry huts