I see where Tex Avery's "Red Hot Riding Hood" is available for online viewing. Until Warner Home Video gets up the nerve to release a complete Avery set, it'll have to do.
The animation of Red, of course, is among the most famous and most-imitated pieces of animation ever. In this and all her subsequent appearances, Red's dancing was animated by Preston Blair, who came to MGM from Disney, where he had animated on Fantasia. He was proud of the fact that instead of using a live-action model, as Disney usually did when it came time to create an attractive human woman in animation, he made up Red's design and movements from scratch.
The reason Red has been so influential is that she really isn't anything like a human woman in design or construction or movement; in her initial appearance, the design of her face could just as easily lend itself to an animal character rather than a human. She conveys the impression of a sexy human being without ever seeming like a copy of one, and therefore without begging the question of why they didn't just do the dance in live action. One of the big questions of animation, from the beginning right up through so-called 3-D animation (it's all 2-D once it's projected on a screen, sez I), is how to create a character who seems like a realistic human being without seeming like a copy of realistic human beings. Blair solved that problem: he came up with a real-world human who was also surreal and "cartoony."
The other cool thing about Blair's animation of Red is that his Disney training shows through even more strongly than usual in some of her acting, so that she seems like a strictly G.I. version of Snow White, or the Disney princess from Hell. And, after all, taking Disney cartoons and sending them to Hell is a pretty good description of Avery's modus operandi at MGM.
Red was a creature of World War II and the unprecedentedly adult cartoons turned out by studios like MGM, Warners, and even Disney (what do kids make of "Der Fuehrer's Face?") during that period. After the War, cartoons started to place more of an emphasis on chase stories and try/fail blackout gags, probably influenced by the success of MGM's Tom and Jerry. Post-WWII, Avery made one more all-new cartoon featuring Red, "Uncle Tom's Cabana," but with a somewhat more demure Red (though it does feature the single best erection gag in the history of cartoons). Preston Blair left not long after that, but Red's dance from "Swing Shift Cinderella" was re-used in 1949's "Little Rural Riding Hood," the last of his great sex-and-violence combinations (which tops "Cabana" by including a joke where the wolf proves to be, as Seinfeld might say, not master of his domain). After that, sex jokes seemed to go out of Hollywood cartoons for a while, and violence reigned alone for a decade or more.