Several factors combine to make Mt. Cook the impressive peak it is.
The weather in the Southern Alps is usually horrible, with massive amounts of snow falling all year round. This makes for extensive glaciers and snowfields with frequent avalanches, and the alpine terrain near the peak is consequnetly difficult. The vertical rise of Mt. Cook is close to 3000 meters on either side of its range, making for a long and tiring approach from the lowlands unless a plane is hired. Edmund Hillary was part of the team that made the first traverse. The usual practice is to get a small plane ride to the Plateau Hut at 2200 meters, then wait there for a window of good weather, which often will not come before you run out of food.