Preheat the oven to 350 degrees F. Chop walnut pieces as small as possible, ideally using a food processor. If you do not have one, I recommend adding walnuts to a sealed bag and then tapping on them with a heavy object to break down. You want the texture of finely chopped nuts, but no need for a powder. The end result should be around 1 cup. Spread on a baking sheet and toast mixture in the oven for 5-10 minutes, until fragrant.   Set aside.

In a stand mixer or with a hand mixer, cream together butter and 1 cup of powdered sugar. Mix until light and fluffy, then add vanilla extract and beat to incorporate. 

Next, add flour, walnuts, and salt, mixing to integrate. You should have a fairly cohesive mix at this point but if not, feel free to add a splash of milk to help things along. Cover mixture and chill in the fridge for 30 minutes. It will firm up as it chills and it will become more easily to mold.

Pour granulated sugar into a shallow bowl. Taking 1 TBS-sized scoops of dough, roll into balls and then roll in granulated sugar, to coat. This will help the powdered sugar stick after baking, Baked for 11-15 minutes, until slightly golden brown. Remove from oven and let cool.

Once cooler, roll each cookie in powdered sugar for a real "snowy" effect. Feel free to re-roll just before serving as well. These cookies can be stored in the freezer for up to one month.