I've been doing some research into early tires, and have found some interesting stuff: Early on, automobile tires, indeed rubber products of all sorts, came in a variety of colors, back in the years before the First World War! Straight gum rubber, of course, had poor wearing characteristics, and it was also very subject to deterioration from ultraviolet light, along with the pollutants stemming from automotive use (grease, oil, even gasoline). Very early on, additives were used to extend the useful life of gum rubber in automobile tires, including zinc oxide, which of course is stark white in color. Zinc oxide gave hardness and durability to gum rubber, in much the same manner as carbon black, and even iron oxide was used. Automobile tires in those early years apparently could be rather colorful--Goodyear Tire & Rubber made their first "Blue Streak" tires (blue sidewalls!) in 1916, along with red sidewall tires as well. Red rubber was, of course, quite common, well into the 1920's (Model A Fords used red rubber for radiator hoses and fan belts straight from the assembly line!), and even the new, 1928 Model A used red hard rubber in their molded steering wheels (keep that in mind should Round2 follow up on a reissue of the AMT 1928 Model A Tudor--they have found the tooling, and have run test shots of it, I was told at NNL East by their representative!!!).
However, regardless of the type of material mixed in gum rubber to extend its serviceable life, carbon black was by far and away the most popular, being the most plentiful and least expensive--it was a common industrial byproduct, as opposed to specially made pigments having other colors. Additionally, by 1910, there were at least one million automobiles and trucks in use in the US, a number that would increase dramatically over the next few years, as Ford was attaining production numbers equal to the entire rest of the auto industry by 1913--with a resulting demand for tires that could be produced quickly and inexpensively.
Another thing I found, which reduces to a myth, is the notion that Ford Motor Company used Firestone tires exclusively--apparently they did not. It sort of makes sense, given the massive production numbers achieved by Ford even by 1914 (when they produced over 400,000 Model T's) that Ford had to source tires and other rubber products wherever they could find them. While I haven't seen them, I read that photo's do exist of Model T's and Model A's coming off assembly lines at times, with tires of different brands ON THE SAME CAR.
So, there is a lot more to the story of tire colors than even I would have imagined. But one thing stands out: There seems to be no definitive date or time when Fords ceased coming with "white" or very light colored tires and settled on black rubber. But then, the concept of annual model or styling changes didn't come about at Ford until 1933, most all changes coming as new parts were designed, and added to the mix on the assembly line, as "running changes".