Finely chopped walnuts are mixed into the dough for these tender butter cookies. Their round shape and powdered sugar coating make them look like balls of snow.
In a large mixing bowl, beat butter with an electric mixer on medium to high speed for 30 seconds. Add granulated sugar; beat till combined, scraping sides of bowl occasionally. Beat in milk and vanilla till combined. Beat in as much of the flour as you can with the mixer. Stir in any remaining flour with a wooden spoon. Stir in nuts.
Shape dough into a 1-inch balls. Place balls 2 inches apart on ungreased cookie sheets.
Bake in a 375 degree F oven for 12 to 15 minutes or till bottoms are lightly browned. Let cool on cookie sheet for 5 minutes.
Roll warm cookies in powdered sugar. Transfer cookies to a wire rack and let cool. Roll in additional powdered sugar just before serving. Makes about 42 cookies.