Preheat oven to 350 degrees F.
In a mixing bowl, beat egg whites and salt to soft peaks, then add sugar and beat again until peaks are stiff. Beat in almond flavoring. Using a rubber spatula or wooden spoon, stir in half of the coconut. Sprinkle in the nutmeg and flour, stir, then fold in the remaining coconut.
Using a melon baller or other small scoop, or working with 2 spoons, form 9 "snowballs" a couple of inches apart on each of 2 cookie sheets. Bake snowballs 12 to 15 minutes, until lightly golden. Remove from oven and garnish each snowball with half a cherry and a couple of slivered almonds. Transfer to a rack or serving plate to cool.