In a large mixing bowl, beat butter with an electric mixer on medium to high speed for 30 seconds. Add granulated sugar and beat until combined. Beat in orange peel, lemon peel, lime peel, 4 teaspoons orange juice, 4 teaspoons lemon juice, 4 teaspoons lime juice, and 1 teaspoon vanilla. Beat in as much of the flour as you can with the mixer. Using a wooden spoon, stir in any remaining flour and the almond flour. Divide dough in half.
Preheat oven to 350 degrees F. On a lightly floured surface, roll each half of the dough to 1/4-inch thickness. Using 1- to 2-inch cookie cutters, cut into desired shapes. Place cutouts on ungreased cookie sheets. Bake for 8 to 10 minutes or until edges are lightly browned. Transfer to wire racks and let cool.
For frosting, in a medium bowl, combine cream cheese, powdered sugar, 1 teaspoon orange juice, 1 teaspoon lemon juice, 1 teaspoon lime juice, and 1 teaspoon vanilla; beat with an electric mixer on medium speed until smooth. Tint with red food coloring. Spread onto cookies. Makes 72 cookies.