Mix shortening, sugar, eggs, and vanilla together in large bowl. Stir flour, salt, and baking soda together in a separate bowl. Blend dry ingredients in with the shortening mixture. Mix thoroughly with hands.
Divide dough into 3 parts; shape into cylinders, 1 1/2 inches in diameter and about 7 inches long. Roll in colored sugar (or use finely chopped nuts instead). Chill for several hours or overnight.
Heat oven to 400 degrees F (205 degrees C). Cut into 1/4 inch slices, and place on greased cookie sheets. Bake for 8 to 10 minutes. Cool.