Super random thought: The vampire could recognize that there was something off about the snow. Either there's something generically "mystical" about the snow that other supernatural creatures could recognize, or...
Mizore has some odd traits that aren't traditionally associated with snow women, including: sharp teeth, pointy ears, vertically slit pupils and actually being made of snow. The the first three are often associated with vampires however - and vampires are also able to turn into mist in some myths. Vampire turns into mist > mist freezes into snow > snow gets shaped into a snow man > snow man spends a year in a freezer (and loses all memory of being a vampire?) > snow man becomes "snow woman?"