Whisk flour, white sugar, cocoa powder, baking powder, cinnamon, cloves, allspice, and salt in a large bowl. Stir orange zest into flour mixture. Mix vegetable shortening and margarine into dry ingredients, using your hands, until mixture is crumbly.
Beat eggs and vanilla extract in a bowl with an electric mixer until foamy; add egg mixture, 1/4 cup orange juice, and 1/4 cup milk to flour mixture and knead dough in the bowl until thoroughly combined and dough doesn't stick to your hands, about 8 minutes. Dough will be stiff. Knead cream cheese thoroughly into dough, followed by walnuts.
Form dough into balls about 1 1/2 inches in diameter and place onto ungreased baking sheets.
Bake cookies in the preheated oven until lightly browned, 12 to 14 minutes. Cool cookies on racks.
Beat 3 tablespoons milk, 1 teaspoon orange juice, and 1 cup confectioners' sugar in a bowl until smooth; gradually beat in remaining confectioners' sugar until frosting is thick and drizzles slowly from a spoon.
Dip tops of cookies into frosting and place frosted cookies on racks with waxed paper underneath to catch drips. Let cookies dry overnight.