What's meant by wishing for a child "as red as blood, and white as snow"?
Solution 1:
Children's author Philip Pullman explains explains the challenges of retelling Grimms' tales:
Imagery and description: there is no imagery in fairy tales apart from the most obvious. As white as snow, as red as blood: that's about it. Nor is there any close description of the natural world or of individuals. A forest is deep, the princess is beautiful, her hair is golden; there's no need to say more. When what you want to know is what happens next, beautiful descriptive wordplay can only irritate.
He then describes "a great and rare exception":
In one story, however, there is a passage that successfully combines beautiful description with the relation of events in such a way that one would not work without the other. The story is "The Juniper Tree", and the passage I mean comes after the wife has made her wish for a child as red as blood and as white as snow. It links her pregnancy with the passing seasons:
One month went by, and the snow vanished.
Two months went by, and the world turned green.
Three months went by, and flowers bloomed out of the earth.
Four months went by, and all the twigs on all the trees in the forest grew stronger and pressed themselves together, and the birds sang so loud that the woods resounded, and the blossom fell from the trees.
Five months went by, and the woman stood under the juniper tree. It smelled so sweet that her heart leaped in her breast, and she fell to her knees with joy.
Six months went by, and the fruit grew firm and heavy, and the woman fell still.
When seven months had gone by, she plucked the juniper berries and ate so many that she felt sick and sorrowful.
After the eighth month had gone, she called her husband and said to him, weeping, 'If I die, bury me under the juniper tree.'
This is wonderful, but it's wonderful in a curious way: there's little any teller of this tale can do to improve it. It has to be rendered exactly as it is here, or at least the different months have to be given equally different characteristics, and carefully linked in equally meaningful ways with the growth of the child in his mother's womb, and that growth with the juniper tree that will be instrumental in his later resurrection.
She spoke the words when unhappy that despite having a prefect marriage, she could not have a baby, try as they might. She was standing in snow and had just cut her finger and was looking at the blood as it fell into the snow.
The baby in this story is born of supernatural origins. When I read it, I interpreted "red as blood" to mean "real-life and fully living", and "white as snow" to mean "beautiful and innocent".
Solution 2:
This part of "The Juniper Tree" is a close relative of "Schneewittchen" (Snow White), which uses almost exactly the same words (in Plattdeutsch and German, respectively), except there it's as black as ebony wood. Translations of "Schneewittchen" that I've seen either leave this as it is or expand it into skin white as snow, lips red as blood, and hair black as ebony.
Arguably this should be under German usage rather than English usage. :)
Solution 3:
"Red as blood and white as snow" is not actually an English idiom, so that makes your question arguably off-topic, except that you wouldn't know that necessarily unless you asked first.
However, the colors are symbolic in the story. You are right that superficially it means wanting a child with cheeks as red as blood, and the rest of her skin as white as snow, but the meaning is deeper. Red is the color associated with life and passion, and white with purity and innocence, so the wish is for a vibrant, healthy child as well as one that has this certain appearance.