The technical grade for the Hornli Ridge (Normal route from Zermatt) is UIAA III which equates roughly to British V.Diff or U.S. 5.4. There would be a few sections harder than this without the considerable aid from the fixed ropes put in place by the Zermatt Guides. This grade is based on perfect conditions of dry, ice free rock on the steep sections. For those not familiar with these numbers the Hornli Ridge includes very sustained scrambling and a few short (less than 25m) pitches (rope lengths) of the lowest grades of rock climbing. These may feel fairly straightforward on a warm day with sticky rock climbing shoes but can feel a lot harder in the cold / dark / with bigger alpine boots and a rucksack on.
The more relevant grade is the overall Alpine Grade of Assez Difficile (AD)
The technical difficulties of the Hornli Ridge are not great. The real challenge lies in the the length and commitment of this magnificent sustained major alpine route. All the hallmarks of a big ‘mixed’ alpine day will be encountered in abundance. A pre-dawn start; intricate route finding; sustained scrambling; short rock pitches; using fixed ropes; loose rock; snow and ice; Descending, traversing, abseiling / lowering in descent. A long day on the hill.