Once the cookies are completely cool, use an electric mixer to beat the butter, sugar and 4 Tablespoons milk until it is smooth. If the icing is not smooth enough or easy to spread, add the additional milk, a Tablespoon at a time and mix it in until the icing is the desired consistency.
Add two to four drops of green gel food coloring to the butter mixture and mix on low until the frosting is the shade of green you want it to be.
Roll a piece of green fondant into a long strip, about 4 inches long.
Use a spatula to spread the green frosting on each cookie, then set the cookie aside so you can move on to the next cookie.
Place one strip of fondant onto each cookie in a circular motion starting in the center of the cookie. Press the fondant into the icing just enough to make it stick.
Trim off any excess fondant when you get to the edge of the cookie.
Continue this process until all the cookies are decorated. If the icing dries too fast, you can always add a little more to the top of the cookie before adding the fondant.