Booking.com's 'Travelling with a pet?' filter, found under Property Type on the search results page, is the fastest way to narrow down a long list of Italian hotels to ones that at least claim to accept pets. It shouldn't be treated as a guarantee, though: the filter reflects what each individual property has ticked in its own listing settings, and the fine print on fees or weight limits can be stricter than the headline badge suggests.
Two extra checks make the filter far more reliable in practice: read recent guest reviews that specifically mention travelling with a dog or cat, and message the property directly to confirm size limits and fees before finalising the booking, especially for larger dogs.