You could also try starting Firefox in its Safe Mode - i.e. with all add-ons disabled - and see if the problem goes away then. If so, it'll be a matter of finding out which add-on is the culprit!
Firefox Safe Mode
If that doesn't work, another thing to try is to create a new profile and see if that lets you use your Hotmail account normally. If you try this, DON'T delete your existing profile!
Creating a new Firefox profile
Incidentally, I'm running Firefox 12.0 and have no trouble with Hotmail.