This marks the end of the Sam/Rebecca baby arc, which had been intended to run through the entire season. Producers dropped the arc due to viewer response. In addition, they wanted to avoid comparisons with Murphy Brown, which at the time was in the midst of an increasingly publicized pregnancy story arc.
The unofficial creed of the US Postal Service is, "Neither snow nor rain nor heat nor gloom of night stays these couriers from the swift completion of their appointed rounds," with the word "heat" sometimes misquoted as "sleet". This supplies the comic context when Cliff walks into Cheers and is asked if he will finish his mail route: "There's too much snow and sleet out there. Besides, it's getting a little dark."
Woody's "Oil Can" joke is a reference to The Wizard of Oz (1939). He also thinks Frasier is imitating The Tin Man when he's freezing.