Red was a pretty common color for Santa/Father Christmas to wear long before Coca Cola even existed. Check out this version Santa Claus, really pretty similar to the modern version, published 24 years before the Coca Cola company was founded.

As the various visual concepts of Santa Claus/St. Nicholas/Father Christmas coalesced into a single character, those ads probably helped push the needle towards red becoming the only color he ever wears, but the concept had already been kicking around in the public consciousness for centuries, and there's no reason why it couldn't have ended up settling on an image pretty similar to what we have now without the help of Coca Cola's commercials.