Preheat oven to 375 degrees F (190 degrees C). Grease a baking sheet.

Cream white sugar, brown sugar, and butter together in a large mixing bowl. Beat milk, orange juice, and egg into the creamed mixture.

Sift flour, baking powder, cinnamon, salt, and baking soda together in a separate bowl; blend into the wet ingredients in the mixing bowl to form a cookie dough. Stir cranberries and walnuts into the dough.

Drop the dough onto the prepared baking sheet by the teaspoonful.

Bake in the preheated oven until the edges are golden, 10 to 15 minutes. Allow the cookies to cool on the baking sheet for 1 minute before removing to a wire rack to cool completely. Sprinkle confectioners' sugar over the cookies to serve.