1) What, exactly, was the message you received when you tried to access webmail, and was it a message from Firefox itself or a message displayed on the webpage you accessed? At what point did this message appear, i.e. before you entered your username and password, after, while trying to load the login page, etc.?
2) What URL are you using to access the webmail? Without knowing where you are, I can't be specific, but judge best for yourself what part of the country you're in, and use one of these URLs if you're not already:
http://webmail.east.cox.net/http://webmail.central.cox.net/http://webmail.west.cox.net/If one of those doesn't work immediately, clear your cookies and your cache, restart Firefox, and try again. Let me know what happens.
Cox techs aren't generally familiar with anything but IE, based on their training, but you shouldn't have a problem with it if you avoid the pages that use ActiveX, of which they don't have a lot anymore thankfully.