The simple but unpredictable answer is when it is not snowing. The best season to explore Mount Everest is during the months of October and November which are the start of the dry season. The next best season to visit Everest is during the months of February through April; this is the end of the dry season.
Extreme temperatures can interfere with cameras and freeze mechanisms. It is important to carry protective gear for any photographic equipment. The easiest and maybe best way to capture captivating images of Mount Everest is to take one of the guided flights around the mountain which provides a variety of different perspectives.