According to the notepad Private Rich uses, it is September 12, 1951.
This episode has the most and longest sequence shots and the fewest scene cuts of the entire series.
In the following season, the series would make history, as the previously forbidden phrase "son of a bitch" was uttered on television for the first time in history, taking place in Season 8, Episode 3: "Guerilla My Dreams" (1979). While unknown whether or not it is equally historic, this episode shows Private Rich's fellow soldier shout "goddammit" while calling for a medic. Though it's easy to read his lips, the audio on the first syllable is muted for censorship reasons. This use of language was likely unintentional; an improvisation by the actor, and the single-take nature of such a special effect-heavy shot likely played a part in the producers' decision to leave the shot in.
This episode begins and ends, after the intro, with an unusual freeze frame during the opening and closing credits.
Although this is the tenth episode of season 7 of the show's 11-year run, judging by the letter Rich is writing it's one year three months into the Korean War. His letter is dated 9/21/51 and the Korean War lasted from June 25,1950 through July 27, 1953.