Coca-Cola is responsible for the red color of Santa’s suit that you see now. Before their ads of the 30’s and 40’s Santa wore green, red, blue or especially purple.
Actually, Thomas Nast may be most responsible for our modern Santa. This image was from the 1880's, and was widely publicized in Harper's Mag. It did not take many years after that for the Santas in other colors to go away...most that we see in other colors are from around that time give or take a few years (and some European postcards). You are right that Coca-Cola took the "Santa" ball and ran (away) with it...in a brilliant marketing campaign.
This is Santa as envisioned by Thomas Nast back in 1881. He actually drew Santa for Harpers for years before that; and had him in red in the 1860's. But this is his most famous "Santa"..look familiar?
He was also responsible for the Republican Party being represented by an Elephant, by the way.