Brenda,
I too was searching for an applesauce frosting recipe when I saw your request. My cake was served at my elementary school many years ago. I was unable to find an icing or frosting recipe, but did stumble upon this filling recipie that sounds like it may be similar. I intend to try it soon. As I'm sure you agree, nothing tastes as good as a memory, but maybe this is the next best thing.Good luck with your search.

I'm soooo sorry! When I left my message I forgot to include the recipe.

APPLESAUCE FILLING

1 1/4 cups applesauce
1/4 cup packed light brown sugar
1/4 cup butter
1 whole cinnamon stick

Cook in a heavy saucepan over medium-low heat until thick and reduced to 1 cup,stirring occasionally,about 20 mins.
Take off heat and to cool completely. When cool,remove cinnamon stick and spread on top of cooled apple cake.

I think I'll double the recipe for a 13x9-inch cake.