I also want to amend that Season 3's DVD does in fact contain "Oy to the World" as noted from this currently out of stock listing at BestBuy: https://www.bestbuy.com/site/the-nanny-the-complete-third-season-3-discs-dvd/9214389.p?skuId=9214389 (Archived link)

The description for the listing (emphasis mine):

Moving back to Wednesdays after a year on CBS' Monday-night lineup, The Nanny inaugurates its third season, offering 27 episodes this year. Fran Drescher continues to head the cast as Fran Fine, the cheekily vulgar nanny in the veddy-proper Manhattan household of widowed Broadway producer Maxwell Sheffield (Charles Shaughnessy) and his three growing children. Although Sheffield's female business partner, C.C. (Laura Lane), has not given up her efforts to strong-arm Maxwell into marriage, it is clear that the master of the Sheffield house is falling in love with Fran. Indeed, in the season-ending finale, Maxwell not only takes Fran along on a business trip to Paris, but also stammers out those three magic words, "I love you" -- just as the "To be continued" title crashes on the screen. In other developments, Fran briefly moves out of the Sheffield town house and into an apartment with her best friend, Val (Rachel Chagall); Maxwell's imperious mother, Elizabeth (Dina Merrill), sweeps into town, immediately demanding that her son dismiss his nanny; Maxwell's shy daughter Maggie (Nicholle Tom) turns sweet sixteen; and in the series' animated-cartoon Christmas episode, "Oy to the World," the leading actors provide the characters' voices in a helter-skelter North Pole fantasy. As in previous seasons, several guest stars appear as "themselves" during The Nanny's third season, among them Elizabeth Taylor, Alex Trebek, Jay Leno, Dr. Joyce Brothers, Eartha Kitt, Burt Bacharach, tennis champ Monica Seles, fashion designer Todd Oldham, the cast of Dr. Quinn, Medicine Woman, and even "presidential brother" Roger Clinton. Most amusingly, Marvin Hamlisch also shows up -- not as himself, but as a fellow who happens to look like Marvin Hamlisch! Breaking into the Top 20 TV programs for the first time this year, The Nanny closed out its third season as America's 16th most-watched series.~Hal Erickson

We are going as per the original broadcast, not as per the current DVD.

And, at that time, this episode was advertised as a special episode, as it was indicated by @banana_girl in this previous content report.

That's why I listed in the original report that it was aired as a special episode at the regular time like any other episode.

@Mathspy said:

That's why I listed in the original report that it was aired as a special episode at the regular time like any other episode.

And this explain why it should be listed as a special episode.

But according to the Contribution Bible:

Special episodes are any episodes that did not originally air as part of a regular, usually numbered season. Sometimes a network will call an episode a "special" episode—as an example, "in this special holiday themed episode"—but still assign it a season and episode number; in those cases, it should not be added to the special season here but, instead, to the season assigned to it by the network.

It even calls out this particular example of "Special holiday themed episode" as a common one

Do you have a proof that it was originally broadcasted as a regular numbered episode? The fact that it was broadcasted at the regular time isn't a proof.

Without this proof, we can't change anything.