Day 1: Schwarzsee, the east face, the Hörnli ridge
We meet in Zermatt in the morning and take the cable car via Furi up to Schwarzsee at 2,583 metres. There is a small lake up here and a chapel built, so the story goes, by two men who survived a snowstorm on this spot. From here we walk.
The Hörnli path climbs the south-eastern flank in long switchbacks. It is a marked route, but not a gentle one: steep, stony, exposed in places, and secured with chains and fixed ropes on the upper section. In return the mountain grows with every step. The east face rises above you, and at some point you see the Hörnli ridge the way the climbers see it: as a line that disappears into rock.
There is plenty of time to stop along the way. I will tell you why the Matterhorn has that pyramid shape, which two continental plates it is made of, what happened at the summit and then on the descent on 14 July 1865, and how a mountain nobody had climbed became the symbol of a country.
In the early afternoon we reach the Hörnli Hut at 3,260 metres. We check in, have tea on the terrace, and then simply sit and look. From here you see across the whole Matter valley to the Weisshorn and the Dent Blanche, and as the sun drops the entire basin turns warm.
Dinner is early, because most guests here are rope teams who will get up at two in the morning. The house goes quiet correspondingly early. It is unfamiliar and it is part of the experience.
About 3.5 kilometres, roughly 700 metres of ascent, two and a half to three hours of walking.
Day 2: Headlamps, the north face, the descent
Somewhere between three and four in the morning the building comes to life. The rope teams have breakfast and set off. If you want, you get up, step outside into the cold and watch them go: a chain of small lights pushing slowly up the ridge, the stars above it. For many people this is the thing they remember afterwards.
Then you can go back to bed until sunrise. After breakfast we descend, but not by the same path. We go down the northern side, and there the view opens onto the Matterhorn north face. Together with the north faces of the Eiger and the Grandes Jorasses it is one of the three great north faces of the Alps, and it looks like something that was never meant to be climbed. From below it looks even bigger.
We continue down across the alpine pastures to Furi at 1,867 metres, with the mountain behind us slowly turning back into a silhouette, and take the cable car down to the village.
If you still have the legs for it, we take the longer variant instead, through Zmutt, an old hamlet of tightly packed, sun-blackened wooden houses where time appears to have stopped. From there on foot all the way to Zermatt. We decide that in the morning, depending on how everyone feels and what the weather is doing, and it costs nothing extra.
About 11 kilometres to Furi, roughly 1,400 metres of descent, four to five hours. Via Zmutt about 14 kilometres and five to six hours.