Thoughts to some of the responses:
I've seen part of an anime that features a tank possessed by the spirit of a cat...
Ghosts aren't adults only stuff by a longshot. I think we all grew up on ghost stories ranging from the frightening to the humorous/fluffy.
If our dearest Princess Zelda is a spirit in this game, I doubt that she's actually dead. I could see her lying in the castle or a temple somewhere in stasis/a kind of sleep while her spirit travels with Link and points out dangers and stuff in a "fairy-like" manner.
Or maybe the spirit is the result of a communications crystal /something like the stone in WW... but instead of just speaking, she comes out as an image ala "Help me, Obi Wan Kenobi, you're my only hope!"
Or, as I said, it could just be oddly colored box art and once all you guys with DS units who can afford to get the game or get it as a gift play it, you'll look back on this little speculation and laugh.
Who knows? Speculation is fun.