Kaz is right in that a director style dates to the silent era. The idea of a real director in animation (not just someone who does all the creative work with the help of assistants) seems to begin approx. in the late 1910s with John Foster's IFS cartoons (I've seen his Katzenjammer Kids cartoon THE DUMMY, which is credited to him, where he casted at least two other animators along with him), the Fleischers on the early Kokos (Dave did not animate, but he worked closely with Max and the animators for planning the cartoon's story and animation), and later on with Paul Terry, who eventually stopped animating on the Fables but regularly contributed to story and the overall creative direction of the studio. During with early 1926 releases, the Fables studio reorganized into the earliest version of a director-lead studio. In fairness, most of these directors went back to the system of doing most the work themselves, besides John Foster (whose cartoons have a very free for all feel in the animation) and soon after Jerry Shields, who usually used two other animators with him in his cartoons. Frank Moser animated almost all of his cartoons from 1926-29 singlehandly to my knowledge, Mannie Davis had a similar reputation but I know he did rely on other animators a little more, and Henry Bailey seems to of been the same. When you watch the different directors and their cartoons, you can see how this effects the gag style in their cartoons, particularly Moser who seemed to care about animating action rather than gags, similar to Jack King later on. When Foster took over Terry's position, the amount of animators per film increased dramatically, and Davis and Bailey had bigger differences in their story style, Bailey particularly leaned towards darker, edgier ideas for his films. I'd love to write more on this subject, but I haven't seen enough Fables to say more