The problem should be with your security settings in IE, but I've just downloaded and installed a new version of Firefox without problems and without any indication of an invalid signature (and I have that set (Tools/Internet Options/Advanced - Security Section: Check for signatures on downloaded programs is checked, Allow software to run or install even if the signature is invalid is unchecked, Check for publishers certificate revocation is checked; IE8, but should be the same in IE7 if you're still running that).

Are you downloading from here: Firefox download?

I've done this several times before (4 previous versions according to my install location) without any problems. I'm running XP/Pro SP3, all latest updates installed.

Unless you have some other security option I can't see why you can't do that.

Mick