The Sinterklaas ritual of candy filled shoes resembles Christmas stockings. In the week leading up to December 5th, the shoes are placed in front of the fireplace and are filled with a carrot, some hay or accompanied by a bowl of water for Sinterklaas' horse. These are exchanged for small gifts of candy.
Grandma's birthday, December 5th, is St Nicholas (Sinterklaas) eve in the Netherlands. It is allegedly the evening before his birthday (like Christmas Eve).
Noelle is the feminine form of Noel, the grenshandel word for Christmas.