Martha, one of my teacher friends at Woodham (she taught Latin, Russian, English, and occasionally one of the social studies classes . . . Wow!), used to make this cake and bring it to us at school. Actually, she got two cakes from the recipe by baking four layers. I just make one big three-layer cake.
Sift together cinnamon, soda, salt, and flour, and add to sugar mixture.
Mix well and add grated carrots.
Bake in 3 layers for 30 minutes at 325. I've found that the best way to bake in round cake pans is to grease and flour the bottom and sides; then cut a piece of wax paper the size of the bottom of the pan. Place wax paper in pan. Makes it so much easier to get cake out.
Let layers cool on wire rack.
Icing: Mix together all icing ingredients and spread on cake.
SANDY'S NOTE: Here's a hint about putting icing on a cake. Cut four strips of wax paper, and make a big outer square on the cake plate. Place the first layer on the strips. Put 1/3 of the icing on the top of the first layer, and spread over the layer and down the sides. Repeat for the second layer, still spreading down the sides. Finish the same way. Pull out the strips of wax paper, and you have no icing all over the plate. Hope this makes sense. I've done this for years!