I would probably look at the west side of Zürich, like "
Affoltern am Albis" and surrounding areas. Rolling hills, lots of woods and farmland, rural, horse-country. Great for dogs, I think. Go a bit further to the west (say between "Ottenbach" and "Muri"), you have the Reuss river, if your doggies like to take a plunge. Muri itself is handy, if you have a car, as it is within a 30 minutes' commute to either Zürich, Zug, Aarau or Luzern, housing is relatively affordable. If you like to commute by train, Affoltern and along its "S-Bahn"-lines is probably better.
Another area, which is surely good for doggies, but more urban and more expensive, would be the area around the "
Greifensee"
But even some parts of Zürich itself, like the "Seebach" or "Neuaffoltern" areas, have spots near the woods or near the "
Katzensee", where your dogs can enjoy, adequate housing is a bit more difficult to obtain and not exactly cheap, though.
These and lots more.
Good luck