The Staples Center and Los Angeles Convention Center (which are right next to each other along Figueroa Blvd. just south of downtown) have lights to illuminate the exterior of the buildings at night. During December the lights have been hued green on both structures. I can only assume this was intended as vaguely holiday themed.
The top of the U.S. Bank tower (formerly known as the Library Tower) in the Bunker Hill portion of Downtown has panels that can display colors. During December, the colors chosen for the panels are typically white, red, and green.
The colors of the Mexican flag. And Cinco de Mayo isn't for months.
The Carl's Jr. restaurant in downtown where I occasionally have lunch was having a promotion where one if one purchased a 44-ounce drink, one got a collector's Coca-Cola cup, available in either red, green, silver, or gold.
I presume the association of green with the holiday season stems from the color of Christmas trees. Red I know comes from the color of what we associate with Santa Claus' suit. I also know that the typical image of "the man with the bag" was codified by the Coca-Cola company (not created, but codified) by the images they commissioned in the early twentieth century for their advertisements (so it's not surprising the cup promotion would include red).
I suppose the importance of the colors flows from the way they enhance "the holiday spirit" and that dwelling on the less than religious origins of some of them doesn't make anyone happier. It is through ignorance that most joy is found, and that's especially true of the time when Christmas decorations are overwhelming every area of our society.
It's a holiday tradition, and why it's a holiday tradition is not something with which we need be concerned.