Christmas cookies tradition started from holiday biscuits in Medieval Europe. They included spices and dried nuts, like many of our Christmas cookies today. Apparently there were strict baking laws (presumably for safety reasons) but the holidays were an exception.
Some say that giving cookies to Santa started around the Great Depression to teach kids generosity. I know someone who was taught all along that Santa actually doesn't like cookies, he likes pizza and beer, so he grew up leaving pizza and beer out for Santa on Christmas Eve. Clever!
We haven't decided about Santa and kids but I wonder what the Santa who comes to our home would prefer... maybe brownies. Edge pieces only-- extra special gifts for corner pieces.