Switzerland's network of staffed mountain huts, many run by the Swiss Alpine Club (SAC), is one of the country's great hiking assets, but dog policy varies significantly from hut to hut. Some allow dogs to sleep in the shared dormitory alongside guests; many don't, for hygiene and space reasons in tightly packed sleeping halls, and may offer a barn, storage room, or outdoor area instead.
Always contact the specific hut directly before a multi-day hike that includes an overnight stay, ideally by phone or email rather than assuming a listing is current. Huts are often remote with limited connectivity, so build in time for a reply.
Lower-altitude alpine guesthouses and farm stays (similar in spirit to Italy's agriturismi) tend to be considerably more consistently dog-friendly than the high mountain huts themselves, and are a good alternative if a hut's policy doesn't work for your trip.