Edit, just read back, turns out others had caught this as well, I'm glad some others got the word and character play. No no. This is so much cuter before translation, Koyuki's name is also a play on her costume. Koyuki can also be interpreted as 'snow child' and there is a legend/myth such as Yuki Onna, snow lady!
Ugh it's such a good play on her character too, since she's super beautiful