Santa Claus is a blend of the legend of Saint Nicholaus -- a bishop, and Father Christmas -- from English folklore.
Each has been depicted in many garbs and colours throughout the centuries, including red, before the traditions blended together.
In the Dutch Sinterklaas tradition, he is definitely a bishop wearing red with gold trim, with a red bishop's mitra and staff.
When people have dressed up in the English tradition specifically, they have often chosen other colours, such as green, to as not be mistaken for Saint Nicholaus or the more modern Santa Claus.
So, no, Coca Cola did not make Santa Claus red. But their image of Santa Claus has been the most influential.