Go down the stairs from the hut to the glacier. Very short descent. Pass the rocks of the Gruenegg at the west side and climb up in the small valley between Gruenegg and the seracs of the Ewigschneefäld-Glacier to reach the upper and even part.. If there is much snow you can go a bit more left and less steep, but there are many crevasses. After P. 3135 (end of the SW-ridge of Gruenegghorn) you climb steep in NE-direction and cross the serac section where possible. North of P. 3537 you climb E over a huge slope until you reach the saddle between Gruenegghorn and Gross Gruenhorn (ca. 3800 m, not mesured in the map).
Note: there is some danger of falling ice from the Gruenegghorn. So do not take a rest too long.
From the saddle turn left and climb the slope under the SW-ridge as high as possible with ski. There are are some culoirs (about 43°) which lead to the summit ridge which is easy to climb;
1300 m ascent, about 5 h
Descent on the same route. If you are an excellent skier and conditions are excellent, you can take your skis to the summit and descend directly over a small and steep slope (100 m with 43°, rated AGAS = extraordinary good alpine skier)
Crampons, ice axe, rope needed
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"Why do climbers rope themselves together? To Prevent the sensible ones from going home!"