Although its 3754-meter elevation is very low by world standards, make no mistake: Mount Cook is one of the most impressive and daunting mountains in the world, right up there with the peaks of the Himalaya, Peruvian Andes, and Mount McKinley.
Several factors combine to make Mount 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 consequently 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 used. Finally, the summit itself is a very steep knife edge that is what remains after the top 10 meters of the summit fell away in a massive landslide/avalanche on December 14th, 1991.
Mount Cook has three summits, all close together along the north-south trending summit ridge, with the north one (High Peak) the highest--the middle peak (3717m) and south (Low) peak (3593m) are slightly lower. Edmund Hillary made a notable first ascent on Mount Cook in his pre-Everest days. Surrounding Mount Cook on almost all sides are scores of other impressive icy giants, such as Mount Tasman, second highest mountain in New Zealand, and Mount Sefton, constantly avalanching snow down it's tremendous southeast face.
As noted above, Mount Cook is one of the most difficult mountains to climb in the world, a suitable goal for only the most experienced and skilled mountaineers. 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. The summit climb features a lot of very steep snow and ice, culminating in the airy knife-edge of the actual summit.
As mentioned in my journal entry, during my visit to New Zealand in 1993 I discovered that guides charged US $1,400.00 to take one climber to the summit, with the guide/client ratio inflexible at 1:1 and no guarantees with regards to the horrible weather. In 2004 an experienced American climber told me that guides will not take you up Mount Cook unless they have climbed with you a great deal in the past. The best bet is to team up with a friend (two-man teams seem to be the standard on this peak), make sure you both know what you are doing, and go for it yourselves. Good luck!