You can choose polarized sunglasses to provide your eyes well protection in such place. However, personally, you'd better wear skiing goggles to shield your eyes. Skiing goggles can protect your eyes well from string and cold wind in everest. Besides, the goggles can also filter glares from snow surface, also prevent the string sunlight. Besides, most of skiing goggles that are made with anti-foggy lenses that can prove you more convenient.
The sunglasse for climbing the Everest should at least live up to the following requirements. First of aal, the sunglasses should be able to screen off the extremely powerful ultraviolet rays on the Everest in case of burned eyes. Secondly, the sunglasses should be able to be frost-proof and antifogging with good perspective effects. Thirdly, the sunglasses should be able to prevent the cold wind on the Everest from irritating the eyes. And the sunglasses should also be able to prevent the eyes from the intense reflection light of the snow which can easily eye strain and snow blindness. For more information about the sunglasses for Everest, you can refer to the following web site first for a more detailed look.
Well, for your situation, maybe there are many choices you can just have a try. But on the other hand, I will just suggest some special sunglasses which can do a good help for you. For example you can just try glacier sunglasses. As we know that glacier sunglasses are specifically designed to protect your eyes from the intense UV radiation that reflects off snowfields and glaciers. And they have dark lenses and side shields to keep UV rays out of your eyes. So it can be very helpful. Also, goggles which can make the difference between reaching the summit and turning around in windy and snowy conditions should be prepared too. Of course, if you need to know more about it, just link to http://www.mountainguides.com/gear-recommended.shtml.