Here is what the Coca Cola Company says:
It's a common misconception that Santa wears a red coat because red is the color of Coca-Cola.
In fact, Santa appeared in a red coat before artist Haddon Sundblom painted him for Coca-Cola advertising.
The Civil War cartoonist Thomas Nast drew Santa Claus for Harper's Weekly in 1862; Santa was shown as a small elf-like figure who supported the Union.
Nast continued to draw Santa for 30 years and along the way changed the color of his coat from tan to the now traditional red. Though some people believe the Coca-Cola Santa wears red because that is the Coke® color, the red suit comes from Nast's interpretation of St. Nick.
The Coming of Santa Claus by Thomas Nast
Snopes also debunks the claim:
BUT:
All this isn't to say that Coca-Cola didn't have anything to do with cementing the modern image of Santa Claus in the public consciousness.
In an era before the advent of television, before color motion pictures became common, and before the widespread use of color in newspapers, Coca-Cola's magazine advertisments, billboards, and point-of-sale store displays were for many Americans their primary exposure to the modern Santa Claus image.