Butter cookies: Beat the butter, sugar, salt, and vanilla extract, using an electric mixer, until light and fluffy, 2 to 3 minutes. Beat in the egg yolks, one at a time, until combined and then add the lemon zest.
Turn mixer down to its slowest setting. Gradually add flour and mix until incorporated, stopping once or twice to scrape bottom of the bowl.
Divide dough into two portions and roll each into a log 2 inches in diameter. Wrap each in plastic wrap and chill at least 2 hours up to overnight.
Preheat oven to 375 degrees F. Line 3 baking sheets with parchment paper. Slice cookies 3/8-inch thick and place on the lined baking sheets giving 1-inch spacing between cookies. Bake, 2 trays at a time, for 14 minutes or until light golden brown, rotating the pans halfway through baking time. Keep the unbaked cookies chilled until ready to bake. Cool the cookies on the baking sheets.
Eggnog Icing: Beat the cream cheese and butter until completely smooth, using an electric mixer on medium speed. Mix in eggnog, alcohol, and nutmeg. Turn mixer down to its lowest setting and gradually mix in confectioners' sugar until completely incorporated.
After the cookies have completely cooled, ice cookies and dust with cinnamon.