Cookies: Beat butter and sugars in a large bowl on medium speed until fluffy. Beat in egg, lime zest and juice. On low speed, beat in flour and corn meal.
On lightly floured waxed paper, using lightly floured hands, shape dough into a 13" long log. Roll up in waxed paper and chill dough 30 minutes. Remove and square off log until it has four flat sides. Wrap log in the waxed paper and freeze for 1 hour or until firm enough to slice.
Heat oven to 350. Line baking sheets with parchment paper. Cut log into 3/8" slices. Place them 1" apart on prepared sheets.
Bake 11 minutes (I had to bake 14 min) or until cookies begin to brown lightly. Cool completely.
Glaze: Whisk sugar and lime juice in a bowl until smooth. If glaze is too thick, thin it with drops of water until it's a spreadable consistency. Whisk in food coloring. Spread on cookies, immediately sprinkle with candy decorations. Let dry on racks until glaze hardens.