I find these pretty sturdy, as long as you stick to basic shapes, (nothing with tails or long necks as far as cookie cutters go).

FAVORITE FROSTED SUGAR COOKIES

3 cups flour
1 teaspoon baking soda
2 teaspoons cream of tartar
1 cup butter, softened (I have used margarine with good results, Imperial or Blue Bonnet brand(stick type))
2 eggs
1 cup granulated sugar
1 1/2 teaspoons vanilla

Sift dry ingredients together; cut butter in with pastry blender or large fork. Add remaining ingredients and blend thoroughly. Chill dough for 20 minutes. Preheat oven to 375 degrees. Roll dough out on floured surface and cut with cookie cutters or glass tumbler dipped in flour. Bake on cookie sheets sprayed with nonstick cooking spray in a 375 degree oven for 8-10 minutes until edges are slightly golden.

This is the frosting I use for these, adjust the milk amount to make spreadable frosting.

COOKIE FROSTING

1/3 cup butter or margarine, softened
3 cups powdered sugar
1 1/2 teaspoons vanilla
About 2-3 Tablespoons evaporated milk (or regular, I think evaporated makes a creamier frosting)
Food coloring, if desired

Beat together butter and sugar. Blend in vanilla and enough milk to make a spreading consistency. Add drops of food coloring if desired. Frosting will firm up some after spreading on cookies.