Definitely set in post-WWII era
I'm now watching the episode "Portrait of Murder" (March 1957), about a local artist with WWII battle fatigue/PTSD suspected of murdering the town veterinarian. Defending the suspect, Dave Shelton, to Roy, Dale says that despite Dave's "experiences in the Second World War, in the concentration camp", she didn't think him capable of killing anyone. (Offhand, I don't know of any other episodes that make such specific reference to the actual story-era.)
So (in answer to a couple of posts elsewhere as to the timeframe of the storyline), that puts it no earlier than mid-40s, and more likely early to mid-50s, the Old West scenic/story elements notwithstanding.
Still, the series is a fascinating blend of the Old West and Post-War eras; it's always fun to pick out anachronisms and indicators.