It's not the cookies, it's the cache - and it will often be your server which sends HTTP headers indicating how long to store the file. The longer a static file is served, the longer a default Apache installation will give as an end date.
For CSS files, you are best using versioning for the file name, so when you change the file you change the file name, forcing the browser to download the new version.
Cache hu I refreshed my browser everthing as it had been at least a couple days since I had viewed the site in firefox. It only downloaded the correct file after I cleared cookies so I figured cookies.