This is an update to my original list.
My Favourite Things from The Sound of Music
This song reminds me of the scene in the woods after she's been scared by the dark shadowed shapes of the trees. When she asks the animals what they would do and starts singing With a Smile and a Song. Well this be an alternative song or whilst she' singing she could be imagining her favourite things. I can also Snow White singing this. It does require a positive sounding vocal so it makes sense.
Earth Angel by Llewellyn & Juliana
Her relationship with the Dwarves. She helped them grow and in return they found happiness and in turn looked after her as best they could and loved her like family.
Fable by Nox Arcana
This is a Grimm Tales Tribute and since this version of Snow White stuck close to the original tale, it's only fitting to include it here. It fits with the scene where she runs terrified into the dark woods from the Hunter.
Songbird by Eva Cassidy
A gentle love theme between The Prince and Snow White with the doves and the sunlight.
Dimension of Love from Tenchi Universe
Reunion with The Prince after she wakes up from death. Snow White recalling their journey to find each other. Being positive that their relationship will be even better than before.