In a large mixing bowl beat butter with an electric mixer on medium to high speed for 30 seconds. Add sugar, cocoa powder, cream of tartar, baking soda, and salt. Beat until combined, scraping sides of bowl occasionally. Beat in eggs 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 into 6 equal portions. Wrap portions in waxed paper or plastic wrap. Chill for 3 hours or until dough is easy to handle.
On a lightly floured surface, roll each dough portion into a circle 6 inches in diameter. Using a knife, cut each circle into 6 wedges. Place wedges 2 inches apart on an ungreased cookie sheet.
For antlers, on each triangle lightly press a pretzel into the upper corners. Press in chocolate pieces for eyes. For a nose, press a red gumdrop into the dough triangle about 1/2 inch from the point.
Bake in a 375 degree F oven for 7 to 9 minutes or until edges are firm. Do not overbake. Cool on cookie sheet for 1 minute. Transfer cookies to a wire rack; cool. Makes 36 cookies.