Update September 6, 2008:
Thank you
Maddy for the award!

Snowballs are a Slovak tradition in our family. (So are kolachy but I didn't make those for Christmas this year. I'll get in trouble for not making them and end up doing them for our New Year's Day dinner.)
As a kid (about Zane's age) I used to help my Baba (grandma) roll these out for hours on end. You shouldn't really make this unless you double or triple the recipe. I triple it.

1 cup margarine (real butter makes them go flat)
1/2 cup powdered sugar
1/4 teaspoon salt
2 1/4 cups flour
1 teaspoon vanilla (I always pour extra in)
1 cup of fine chopped walnuts, packed tight (you can't do it with pieces, stick them in the food processor--they need to be like a thick powder)

Cream butter and sugar together.
Baba's recipe says to sift the flour--I'm sure this makes a great difference but I've lost my sifter and haven't replaced it so I've been skipping that step for years now.
Add salt to creamed mixture, work in vanilla and nuts--I use a spatula for this part.
Add sugar and butter stuff to the flour. Don't bother trying to use a spoon, get both hands in the bowl and mix it up until it looks good and mixed.
Chill about an hour. (Ok, I usually skip this step, too.)
Roll into little balls.
Bake at 375 for 15-20 minutes. The tops won't look much different, you'll have to pick up the cookie and peek at the bottom, they'll be done when the bottom is a nice golden brown. Don't under cook them, they'll be doughy. Trust me.
While they're still warm, roll them in powdered sugar. Then a little bit later, roll them again. Don't skip this step.

If you're making a triple batch, buy a pound of shelled walnuts and put them through your little chopper or food processor. It'll come out to exactly 3 packed cups and that's what you want!

Then let me know how much you love these things! They're so addicting!