In a large bowl beat butter with a mixer on medium to high 30 seconds. Add granulated sugar, baking powder, and salt. Beat on medium 2 minutes, scraping bowl as needed. Beat in one of the eggs and the vanilla. Beat in flour until combined.

Divide dough into thirds; tint one portion red and one portion green with food coloring. Leave remaining portion plain. Wrap each portion in plastic wrap; chill 30 to 60 minutes or until dough is easy to handle.

On a lightly floured surface roll each portion into a 12-inch rope. Place ropes side by side. Twist ropes together; lightly roll into a smooth log. Combine remaining egg and the water. Brush over roll. Place decorating sugar on a sheet of parchment paper; roll log in sugar to coat. Wrap in plastic wrap; chill until firm enough to slice (1 to 2 hours in the refrigerator or 30 minutes in the freezer). 

Preheat oven to 375°F. Use a sharp knife to cut log into ¼-inch slices. Place 2 inches apart on ungreased cookie sheets. Bake 7 to 9 minutes or until bottoms are light brown. Cool on cookie sheets 2 minutes. Remove; cool on wire racks.