Booking.com's 'Travelling with a pet?' filter works the same way in Switzerland as anywhere else: it surfaces properties that have marked themselves as pet-friendly, but the details behind that tag — fees, size limits, which rooms qualify — are set by the property, not standardised by the platform.
Read the property's own pet policy on its listing page before booking, and if it's vague or missing, message the host or front desk directly to confirm the fee and any restrictions in writing.
This matters more in Switzerland than in many countries, simply because fees can be a meaningfully larger part of the total bill given the country's general price level — a fee that seemed trivial elsewhere can be a genuine line item here.