The primary reason a mountain climber needs an oxygen mask when climbing Mount Everest is that they are at a high altitude where the air is thinner. As elevation increases, the atmospheric pressure decreases, which means there is less oxygen available in the air. At the summit of Everest, the oxygen levels are only about one-third of what they are at sea level, making it difficult for climbers to breathe adequately.
While cold temperatures can also pose challenges, the main issue with high-altitude climbing is the reduced availability of oxygen, which can lead to altitude sickness and other serious health issues if climbers do not supplement their oxygen supply. Therefore, an oxygen mask helps climbers breathe more easily and perform at higher altitudes.