In a large mixing bowl, beat butter with an electric mixer on medium to high speed for 30 seconds. Add granulated sugar and beat until combined. Beat in lime peel, the 1/4 cup lime juice, and 1 teaspoon vanilla. Beat in as much of the flour as you can with the mixer. Using a wooden spoon, stir in any remaining flour and the nuts. Divide dough in half.
Preheat oven to 350 degrees F. On a lightly floured surface, roll each half of the dough to 1/4-inch thickness. Using 1- to 2-inch cookie cutters, cut into desired shapes. Place cutouts on ungreased cookie sheets. Bake for 8 to 10 minutes or until edges are lightly browned. Transfer to wire racks and let cool.
For frosting, in a medium bowl, combine cream cheese, powdered sugar, the 1 tablespoon lime juice, and 1 teaspoon vanilla; beat with an electric mixer on medium speed until smooth. Tint with green food coloring. Spread onto cookies. Makes 72 cookies.