In a mixing bowl, whisk egg whites and vanilla extract with an electric mixer on low speed, until foamy. Slowly add in powdered sugar until the shiny and stiff peaks form.
Divide icing into separate bowls for desired icing colors. Mix in a pea-sized amount of gel food dye until blended. Pour each color into separate piping bags, fitted with a #2 icing tip. (Pro tip: place bags in a large glass and roll down the bags to make a cuff before pouring in icing.) Twist top of bags to seal off, holding the thickest part of the icing bag to squeeze out icing. Hold near the bottom at the tip with other hand to smoothly decorate your cookie.
Create an icing outline on the sugar cookies first. If using the pattern tool, fill in patterns with royal icing. Add zig zags, polka dots, and stripes. Make sure to add hems and collars to the ugly sweater cookies for a finished look.