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I think you have to have been born in the South to understand this, but there is a real connection with Southerners between Christmas and snow. It's almost as if snow validates the holiday. Maybe we're just more romantic than people in other parts of the country, and we've really bought into the idea of a "white Christmas;" but every year, the entire South prays that it will snow on Christmas Eve. It's not that we have horse-drawn sleighs anymore, as many Yankees would like to think; but we do like to remember them. Snow reminds us of how Christmas once was, a time of graciousness and charity. We wish we could get back to that, but we never do. And so the promise and joy of Christmas are always followed by a feeling of unfulfillment and melancholy. Snow softens that.
The other reason snow is so important to Christmas is because Christmas is a medieval, European holiday in origin, and therefore needs medieval, European symbols to support it. The birth of Jesus took place in an arid, Eastern country. It's very difficult for Westerners to wrap their heads around the birth of a Savior in such a foreign place. So we wrap the story in things we understand, like snow and Christmas trees and candy canes. Snow is like a white security blanket that we hold next to our heads as we suck our thumbs and gaze at the Nativity. Snow represents the purity of Christ that He has so graciously clothed us with. When we twist that image together with one of His righteousness - something else He's clothed us in - we have the red and white of the candy cane, a beautiful medieval image that, like snow, helps to comfort and encourage us at Christmastime.
The great reformer Martin Luther introduced the Christmas tree into our tradition. But other than it, most of our holiday symbols are medieval and all point back to Christ and what He was born to bring:
"Though your sins be as scarlet, they shall be white as snow." Isaiah 1:18
Christ's sinless blood washed away our sins, which were as red as scarlet, and made them as clean and pure as His own. That is the gift of a tiny baby sent from Heaven and born into an evil world. The Wise Men's gifts of gold, frankincense and myrrh pale in comparison.