Don't worry about your translation being lame (which it isn't), since you've basicly got all the major points down.
My translation:
"I'm sorry" said the snow
"I want to melt into water and go far away and play" the snow said while looking up
"Since I'm in the shadows of the bamboo, I can't melt" he/she said sadly
And welcome to the club science12nerd and mabel.