I discovered this last Christmas during a festive quiz, in which the following question was asked: "The iconic red-and-white Santa Claus image was introduced by Coca-Cola. True or false?"
And all the smart-alecs who had heard the famous rumour thought it was true... but contrary to popular opinion, it is actually false.
You can read a whole long document about why it is false here.
But the short version is that Coca-Cola hired an artist called Haddon Sundblom in the early 1930s to create some memorable drawings of a red-and-white Santa Claus drinking coca-cola. However, images of a red-and-white Santa existed much earlier than this, drawn by artists such as Thomas Nast and Louis Prang.
Nast created a red-and-white Santa Claus caricature for the Harper's Weekly newspaper in 1863 and later drew the 1881 drawing: Merry Old Santa Claus. Furthermore, Prang introduced the custom of Christmas cards and issued a red-and-white Santa Claus card in 1886, which you can see here. Clearly these pre-date the Coca-Cola creation.
Obviously, this isn't too say that the Coca-Cola Claus didn't cement the red-and-white Santa into the popular culture zeitgeist.
But Coca-Cola certainly isn't the reason why Santa Claus is red-and-white.