As with Airbnb everywhere, whether pets are welcome in a Swiss listing is entirely the host's decision, stated in the House Rules section of the listing. Some hosts explicitly welcome pets and even list local dog-walking routes; others don't allow them at all.
If the listing doesn't mention pets either way, message the host before booking rather than assuming — Swiss hosts, like anywhere, can and do decline a booking after the fact if an undisclosed pet shows up, and cancellation in that situation is rarely in the guest's favour.
Ask specifically about any cleaning fee for pets, and whether the property has a garden, balcony, or is within easy reach of a park — useful details for planning a dog's routine in an apartment stay.