Yes, you should put everything in the theme you're using. A lot depends on it's file organization. Basically you can put it anywhere in theme's scope, but it's good practice to maintain order in themes files, like have specific folder for images, scripts, views and other file types. Usually this structure is recognizable in the theme itself, so I advice you to hold to the structure.
But as I don't know your theme - for sake of this question lets create a folder called
intro where you put all files related to intro. Then you might want to redirect to it from
functions.php level. In very beginning of
functions.php file I'd paste following code:
if (!isset($_COOKIE['visited'])) /* if the visitor is a new */
setcookie('visited', true, time() + 3600 * 24);
Where index.html or index.php would be file with animation you've created.