Sift flour, cinnamon, and salt together into a large bowl.
Beat butter with an electric mixer, then gradually add 2 cups sugar and beat until light and fluffy. Beat in 2 eggs, one at a time, then alternately beat in dry ingredients and wine about one-third at a time. Dough will be very soft.
Divide dough into 5 equal parts, flatten, wrap in plastic, and refrigerate overnight.
Preheat oven to 350F. Roll out dough about 1/4-inch thick on a lightly floured work surface. Cut with cookie cutters, transfer to greased cookie sheets. Scraps may be gathered, rechilled, and rolled one additional time.
Brush cookies with remaining egg, sprinkle with a little of remaining sugar, and bake in batches until golden, about 20 minutes. Transfer cookies to a wire rack and cool completely. Decorate as desired and serve. Store in a cookie jar. Cookies taste best after sitting one week.