The first two Lemmings games with a holiday theme were demos only with the title Xmas Lemmings.
Xmas Lemmings 1991 - No full game was released, only a demo. This was an advertising promo for their new game "Oh No! More Lemmings" and included 2 levels with a Christmas theme plus the first 2 levels from "Oh No!".
Xmas Lemmings 1992 - Again Psygnosis called this a demo, and no "holiday themed" full game was released. The 1992 demo contained 4 levels of play.
Holiday Lemmings 1993 - Both a demo (with 3 levels) and a full game (with 16 levels and 2 difficulty choices) were released.
Holiday Lemmings 1994 - Again a demo (with 4 levels) and a full game (with 16 levels and 4 difficulty choices) were released.