My friends etc always say "It's not Christmas until you see the Coke ad" in reference to the build up to Christmas.
However, they weren't the first company to do so as in 1915 and 1923, White Rock Beverages used a today's version of Santa (Red & White) to sell mineral water and ginger ale respectively.[4]
[1] http://www.coca-colacompany.com/topics/heritage
[2] http://www.vintageadbrowser.com/coke-ads-1930s/3#ad5w0neuut0...
[3] http://www.vintageadbrowser.com/coke-ads-1930s/3#aduieywoavp...
[4] http://www.bevnet.com/news/2006/12-18-2006-white_rock_coke_s...
Santa already had a red coat with white trimming - at some unspecified point in the past he did have a green coat.
Coke took an already-popular meme with no trademark and co-opted it for their own marketing, popularising it even further. The expansion of the Coke-themed Santa led to the belief that they invented it.
Something to absorb for those who are trying to work out how to market things.
I know all this because up until 10 days ago I also thought that Coke invented Santa, until I realised I should fact-check that, and found out I was wrong.
Google it yourself. You probably are in a better position to verify it than I am, with my wonky android browser freezing up and saying "bite me, bitch" on a regular basis.