I cheated and used Alton Brown's Sugar Cookie recipe. Its a very forgiving and kid friendly dough. I like them fairly thin and crispy. I usually roll them out to about 1/8" and I bake them on a silpat. Makes for crispy golden brown bottoms and no sticking. The 1 deviation from the recipe is that I cooked them at 350F for about 8 minutes. The baking time will vary depending on the size and shape of the cookie.
The icing is a Powdered Sugar Icing. Its not as firm as Royal Icing when it sets up. It also has a nice sheen to it when dry.
2 1/2 Powdered Sugar
1/2 tsp Vanilla Extract
1 TBS Butter
2 TBS Water
1 TBS Light Corn Syrup
Combine sugar, corn syrup, vanilla, and butter into a bowl. Mix on medium and slowly add the water until the icing is the desired consistency. Color how ever you wish.
I used paste colors for the blue. The paste color is more intense than the liquid food coloring. They don't add extra moisture to the icing, so it doesn't impact the consistency. Huge warning though, a little goes a long way. I colored about a cup of blue icing with just a dot on the end of a toothpick.
I dipped the cookies into the icing then set the cookies on a rack. Once the icing set, I came back and piped more icing in a contrasting color. I also like the additional texture it gives.
As for the ones that are decorated with sanding sugar. I brushed them with either corn syrup or blue icing gel, then dusted them with white sanding sugar. I used a larger pearl variety because I liked the texture.