Switzerland doesn't have a national rule either allowing or banning dogs in restaurants — like Italy, it's left to each business. In practice, outdoor terraces are welcoming almost everywhere, often with a leash hook built right into the railing or table leg.
Indoor seating is more variable, and tends to depend on the type of place: casual cafés and mountain-hut-style restaurants are generally relaxed about it, while more formal dining rooms are less predictable. A quick question at the door resolves it either way.
Cities with a strong outdoor café culture — Zurich's Niederdorf, Geneva's old town, Lausanne's lakefront — make it easy to default to terrace seating with a dog in good weather, which sidesteps the question entirely.