In the last original episode, The Gun Slinger, Rob as the sheriff rides a horse up to his office. That certainly seems to have been shot on a studio's outdoor Western set. Was anything else in the show shot outdoors?

As far as I can remember that was the only one.

There were short scenes in "Br-rooom Br-rooom" and "Brother, Can You Spare $2500?" that take place outdoors but they were obviously filmed on a studio stage.

An excerpt from Vince Waldron's Dick Van Dyke book....

>>>But only a handful of episodes let characters undertake movement outside. These include “The Attempted Marriage” (episode # 34), “My Husband Is a Check-Grabber” (episode # 50), “Brother, Can You Spare $2500?” (episode # 110), “100 Terrible Hours” (episode # 122), “Br-rooom, Br-ooom” (episode # 125), and – making use of one of standing sets from Gunsmoke -- “The Gunslinger” (episode # 158). <<<

A bit more on the subject can be read at the books Facebook page

https://www.facebook.com/DickVanDykeShowBook/posts/the-great-outdoors-in-the-dick-van-dyke-show-one-of-the-ironies-of-the-use-of-sp/1507201365970925/

If you don't do Facebook but own the book, I tried to find the section in my copy of the book, but I can't find the pages

The way I remember it, all the outdoor scenes were shot on a sound stage with the exception of the Gunslinger episode.