This month, two of the finest examples are on display in New York. In “George Balanchine’s The Nutcracker” at New York City Ballet, dancers gleam like ice princesses as they flit across the stage in brisk petit allegro jumps under a steady snowfall that eventually reaches blizzard proportions. And in “The Hard Nut,” by Mark Morris, the dancers, male and female, throw snow while dashing across the stage in sleek formations. The effect in both is a thrilling merging of motion and music.