For a boy this makes me think of a very feminine guy who probably wants to be a girl. Not a good name for a boy at all. For a girl, it makes me think of a sensitive girl who cries after she gets teased. Not a good name for either gender.
This is an equally pretty name for both boys and girls, although I could never use it, because I am American, and people would just think I am a thoughtless otaku. I always think of Yuki Sohma from Furuba, who was nicknamed "Yun-Yun" (which I love) by his friend, Nabe-chan.
At first, I thought that Yuki was a boy's name because of Yuki from Fruits Basket (he was the first person, real or fictional, that I knew as having the name). I think Yuki is a cute name for both genders, though probably a child with the name Yuki ought to be a girl, because apparently it's really a girl's name. If I were going to name something Yuki, it would probably be a character in a story or a pet (probably a rat, because of Yuki from Fruits Basket).