Monet is referred to as a 雪女/yuki-onna, literally ‘snow woman’, both in dialogue and narration/chapter titles. In addition to being literally accurate, the yuki-onna is a type of Japanese yokai, a female spirit of winter and snow.
There’s quite a few folktales about the yuki-onna, and they tend to vary from region to region, but a couple that struck me as relevant here specifically are that 1) she’s said to float, rather than walking and 2) she dissolves into a cloud of mist or snow when threatened.
There is also a myth about her requesting travelers hug a child, only for the child to turn cold and heavy and slowly cover the traveler with snow and freeze them to death, which rings very similar to her attempt to freeze Luffy to death by embracing him.
