The fact that you don't use IE doesn't get rid of some of the vulnerabilities as IE is integrated deeply into the Windows OS.
You will need IE in order to connect to windows update (as Eddy stated, you need to patch your OS) in order to get your OS patched. So regardless of if you use IE on not, you need to keep IE up to date. Untill MS removes integration from the OS and allows other browsers to connect and update the OS (don't hold your breath), you will need IE.
Connecting to the windows update site without IE (or some of the IE based browsers, Avant), it won't work as MS uses activex and Firefox doesn't support activex.