Preheat oven to 300 degrees F.  In a large mixing bowl, cream the butter together with 1/3 cup of powdered sugar.  Add the vanilla and flour and blend until smooth.  Mix in the walnuts.  Place the remaining 1 1/3 cup powdered sugar in a medium bowl and set aside.

Scoop dough in rounded teaspoons and roll between palms to make a smooth ball.  Place about 1 inch apart on a parchment lined baking sheet.

Bake for 15-20 minutes, until cookies just begin to brown around the edges.  Gently roll cookies in powdered sugar and set on a wire rack to cool.  When completely cool, coat cookies again with powdered sugar.

To make Snowmen:  slowly and gently slide a toothpick down through the top of a cookie.  Make sure there are equal lengths of the toothpick poking out of the top and bottom of the cookie.  Push the bottom portion of the toothpick into the top of a second cookie, and the top of the toothpick into the bottom of a third cookie.  Decorate with mini chocolate chips, frosting, or any other candies.  Make them as simple or as ornate as you like, and have fun!