One thing I have always enjoyed about camping in the snow - winter or spring - is that you can have what I call the feeling of being "out there" so much more easily. To me this is a sense of isolation and remoteness, of being in a place where few people ever go. In the summer it's hard to find a place that has that feeling, but when the snow covers the ground it's just a short distance from the road.
Plus, it's always so interesting to see a place in the winter that you've seen in the summer, and to appreciate the enormous difference.