Beat butter at medium speed of an electric mixer 2 minutes or until creamy. Gradually add sugar, beating well. Add egg, and beat well. Combine flour and next 3 ingredients. Add to butter mixture, beating at low speed just until blended. Stir in vanilla.
Roll dough to 1/4" thickness on a lightly floured surface. Cut with decorative 3" cookie cutters. Place 1" apart on ungreased cookie sheets. Bake at 350° for 9 minutes. Cool completely on wire racks.
Spoon about 2/3 cup white Royal Icing into a decorating bag fitted with decorating tip #3 (small round tip). Pipe white icing to outline cookies and to outline detail desired inside cookies.
Divide remaining Royal Icing into a separate bowl for each color desired; color as desired with paste food coloring. Slowly stir just enough water into each bowl of icing to make "flow-in icing" that is still thick but flows into a smooth surface after stirring. (Add water a little at a time; if flow-in icing is too watery, it may not dry properly and may run under outline into another color area.)
Fill decorating bags (using no tips) about half full of flow-in icing. Snip off small tip of cone. Pipe desired colors of icing to cover areas between the Royal Icing outline; spread icing into corners and hard-to-reach areas using a wooden pick, as necessary. Add flow-in icing 1 color at a time, allowing icing to dry before changing colors. Avoid using excess icing, or it will spill over into another color area. If air bubbles form in icing, use a sterilized straight pin to remove them. Decorate with assorted candies and decorator sprinkles while icing is still wet.