There is a Russian folktale about a couple who wants a child and they don't have one, so they go out in the snow and make a snow child, and it comes to life.
http://www.pitt.edu/~dash/type0703.html
I know about this because I read the novel "The Snow Child" by Eowyn Ivey, which is a modern retelling of the story.
Clicking around on the site above, it looks like there are several myths where a woman eats an icicle and gives birth to a snow child. Could that work for you??
eP