How did Krakauer try to prevent damage from solar radiation in Into Thin Air?

The word "radiation" scares a lot of people because they don't understand what it is actually referring to. Electromagnetic radiation and/or solar radiation refers to the entire spectrum of light. This includes radio waves, microwaves, infrared waves, visible light waves, ultraviolet light waves, x-rays, and gamma waves. Earth's atmosphere and magnetic field protects organic life from a great deal of the most harmful forms of radiation that constantly bathe the planet. Of course, ultraviolet light still manages to penetrate to Earth's surface and cause things like sunburn. That is a realistic danger of solar radiation. You can protect yourself from it by wearing sunscreen, limiting exposure time, and covering skin.
Krakauer and the other Everest climbers worry about the exact same UV radiation dangers. The problem is that they are so high in elevation and the atmosphere is so thin at that point that the UV danger is extremely high. Sunburn and retinal burns are real concerns, and the retinal burns can become life-threatening. Blind climbers are not likely to get down the mountain. Krakauer's protection on the mountain isn't that different than protection somebody would want in a hot desert.
Krakauer makes sure that no skin is exposed. This protects his skin from the freezing temperatures, as well as the solar radiation. To protect his eyes, he wears goggles that don't allow UVA or UVB light to penetrate.

Even though it was a cloudy day, the vicious ultraviolet radiation at this altitude would render him snow-blind very quickly. "Stuart! " I yelled over the wind, pointing at my eyes. "Your goggles!"