In reply to gavinpeach:
I just did the Matterhorn .. like 2 days ago ... Lion-Hornli ... my first time on this mountain.
Apparently you are allowed to bivi below the metal stairs someway below the hut... it was all very DRY!! you have to be a long way down to be near a water supply or carry all you need. The 'protocol' that I have heard of but not experienced, is the local guides, then other guides then 'others' have controlled departure from the hut AND even people who are starting from a bivi can be questioned (simply do not believe that someone can start from so low).
The hornli ridge is simply not pleasant to climb and not easy to find your way even in daylight let alone night ..... in fact you might be better off slotting in behind a few guides and following the head touches.
OR ...
do it from the Italian side where the rock is way way better (not saying much). To do that you need to contact the local guides office in Cervinia to book a space in the bivi hut 30E each includes bed, blankets, gas and pots. You definitely need to take water from 200m below the col. Lion, we were using some very old snow/ice near the hut (not nice). Hut approach is quite pleasant too