In a mixing bowl, beat butter and shortening with an electric mixer on medium to high speed for 30 seconds. Add sugar, cocoa powder, baking powder, and salt. Beat until combined, scraping bowl occasionally. Beat in egg and vanilla until combined. Beat in as much of the flour as you can with the mixer. Using a wooden spoon, stir in any remaining flour. Divide dough in half. If necessary, cover and chill dough about 1 hour or until easy to handle.
Preheat oven to 350 degrees F. On a lightly floured surface roll, half of the dough at a time until 1/4 inch thick. Cut with a a 2-inch triangular cookie cutter. (Or shape each half of dough into an 8-inch square. Cut each square into sixteen 2-inch squares. Cut each 2-inch square in half diagonally to make 64 triangles total.) Place triangles 2 inches apart on an ungreased baking sheet.
Bake for 8 to 10 minutes or until edges are light brown. Transfer to wire racks and let cool.
For each reindeer, pipe a little frosting on two pretzels; attach to the long side of each cookie for antlers. Use frosting to attach a cherry half to the opposite point for a nose. Pipe two dots of frosting for eyes. Let stand until frosting is set. Layer cookies between waxed paper in gift container; cover.