In Eastern Europe Saint Nick is often portrayed with heavy furs, which are brown. Or in very thick winter clothing. If he is portrayed in colors, blue is usually his color of choice. Because blue is associated with winter and frost.
Coca-Cola didn't invent the modern Saint Nick, but they did a hell of a job to popularize a version of him that matched their color scheme. You don't see Saint Nick associated with Heineken for example. Or Mountain Dew.