Place confectioners' sugar, water, powdered egg whites and vanilla in large bowl. Beat with electric mixer on high speed 5 to 7 minutes until stiff peaks form and icing is fluffy and glossy.
For each color of icing, place 1/2 cup icing in bowl. Stir in 3 to 4 drops food color until evenly distributed and icing is smooth. Add additional drops food color until icing is of desired color. (Keep remaining icing covered with a damp cloth to prevent drying.)
To ice cookies, place cooling rack on foil-lined baking sheet. Spoon icing onto cookies using a teaspoon. Cookies can also be iced using a new small paintbrush. Place iced cookies on cooling rack to dry.
Use contrasting icing colors to decorate iced cookies, if desired. Place small amount of contrasting icing in small resealable plastic bag. Snip off tiny piece of the corner of the plastic bag. Create design by squeezing contrasting icing onto cookies. Allow iced cookies to dry thoroughly before stacking.