Cream the butter, salt and sugar with a stand mixer (paddle attachment) or hand mixer until light and fluffy.
Add the egg and vanilla while mixing. Scrape down the sides of the bowl.
Add the flour and mix until incorporated.
Shape the dough into a disc, wrap it and refrigerate for at least 1 hour.
On a lightly floured surface, roll the dough to about ⅛ inch thick. Cut out trees with the cookie cutter and cut rectangles with a knife for presents.
Place the cookies on a parchment-lined baking sheet and bake at 350°F for 10 to 12 minutes, until the edges just turn golden brown. Cool completely.
For the icing, beat the egg whites and confectioners' sugar until glossy. Divide among small bowls and tint with the gel food coloring. Keep any icing not in use covered with plastic wrap.
Transfer the icing to piping bags and decorate. Let the cookies sit 6 to 8 hours or overnight until the icing sets.