You should view the rendered source of the page and see what is rendered (ie you need to look at the actual markup and CSS classes on the markup) and you need to master CSS selectors and the use of Firebug then you will be able to style anything any way you want and understand why styles are applied or not.
Just because a CSS class exists in markup does not mean it always exists in the CSS files of skins. Classes just provide extra hooks to make it easier to devise selectors to select what you want but in any given skin specific classes may or may not be used in any selectors.
Those links will use whatever CssClass you put on them, if you leave it blank they use the class "sitelink" which is commonly used in most of our skins for header link style. Seems like if you just specify a CSSClass that is not used for anything and does not have any style rules then it will probably use the .art-footer a styles assuming you have them wrapped in a container div with the class art-footer.
Hope that helps,
Joe