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 CokeĀ®
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.