No, I don't think they are wearing the glasses just for cool but for some reasons. These climbers need to climb very high mountain so that they need to protect themselves from possible damages. If the mountain is high enough, it is quite possible topped with snow. The light would become glare after reflexed by the snow. It might cause blindness temporarily or permanently. Sunglasses would effectively provide the protection from glare. Meanwhile sunglasses could provide eyes protection from UV radiation and winds.The higher the mountain is, the thinner the air is. So sunblock is necessary too. As the air is thinner, UV radiation is strengthened. It can easily burn our skin and more damages are possible. So if you need to climb mountains or go to beaches, it is better to wear sunglasses and sunblock.
Commonly, most of people who climb mountain in sunny day. So, wearing sunglasses can protect eyes from sunlight and UV lights. And the same to sunglasses, sunblock is used to protect UV light in the sun. In fact, they are really necessary. It has been proved that long time exposed in sun with naked eyes will contribute to cataracts. As for the skin, long time expose in the sun can burn the skin even cause skin cancer. So, they are not just for cool. But for health.
OK, looks like you just want to know why they just do so. Anyway, shall I remind you that on sunny days, the UV index could be pretty high, not only can it make you hard to see things clearly, but it would do harm to your vision, even make you suffer losses of vision. With a pair of nice and good sunglasses, people would simply get rid of those harmful lights and enjoy their trips. By the way, sunglasses also make them appear cool!
Yes, a lot of mountain climbers wear sunglasses and sunblock. Although wearing sunglasses will make them look so cool, wearing sunglasses could also make their eyes protected from the uv rays in the strong sun lights. As we know, the sun lights are stronger at the top of the mountain than that at the bottom side. They wear sunblock just for the protection from the uv rays at the skin. All these are the necessity for the mountain climbers.