Sparkling snowflakes, delicate dewdrops, hot chocolate from Spain—all of these soul-warming things share a part in the New York City Ballet’s production of “The Nutcracker,” a ballet that elicits nostalgia for those who have grown up watching it or a feeling of holiday cheer for those who are seeing it for the first time. Everyone has her favorite part; mine is the romantic pas de deux at the end of the second act. Choreographed to Tchaikovsky’s passionate and sometimes heart-wrenching score, the scene is full of intense emotion despite being part of a lighthearted children’s ballet.