I believe in The Day The Earth Froze, there are some quest elements, with the girlfriend having been stolen, and the hero being forced to do certain tasks to free her, the witch who is searching for the SAMPO, and then when the sun is stolen, the goof villagers have to quest to stop the evil witch!

http://www.kiddiematinee.com/d-dayfroze.html

And here is some info on the Singing, Ringing Tree, but darned if I can remember if it involved a quest or not!
http://www.thechestnut.com/srtree/srtree-index.htm