Heat oven to 350°F. Grease and flour three 9-inch round cake pans. Set aside. In medium-size bowl, beat eggs slightly; add sugar. Mix in cocoa and food coloring. In a large bowl, combine butter and egg mixture; mix well. Sift flour and salt onto waxed paper. Add to butter mixture alternately with buttermilk. Blend in vanilla.
In a small bowl, combine soda and vinegar and add to mixture. Pour into prepared pans. Bake at 350°F for 20 to 25 minutes or until tests done.
Combine egg whites, sugar, water, corn syrup and cream of tartar in the top of a double boiler or a medium-size metal bowl placed over a saucepan of simmering water. Cook for 5 to 6 minutes, beating constantly with an electric mixer, until icing is white, billowy and registers at least 160°F on an instant-read thermometer. Add marshmallows; stir until melted. Fold in coconut and nuts. Let stand 5 minutes, then frost cooled cake layers.