You won't find many Linux users on Hotmail. You might do better to ask a
Windows forum as Firefox works in Windows too. If you have java installed
then it should not be the problem. It is more likely that Microsoft is
changing web standards arbitrarily as they are prone to do to keep other
browsers at a disadvantage. This is only opinion as I do not use Hotmail or
anything Microsoft.

What version of Firefox are you using? A quick google search
suggested this is a bug that was created with 3.6. Clearing system
cache and cookies seemed to be a temporary solution for some. Others
suggested switching from rich to plain text as a workaround. If you
can setup your hotmail account to be checked through thunderbird or
evolution, you would probably be fine too... Not sure if MS allows
that though.

3.6.3, what do you mean by clearing system cache? I only clear the internet
browser cache.

Yep, I mean internet browser cache. Just made a mental typo.
Granted, I was only repeating what I saw on some of the sites. I did
a google search with the terms "hotmail include original message in
reply" and browsed a few of the responses since I wasn't able to
replicate it on my hotmail account (I don't actually use that account
anymore other than a junk email for registration on various sites).

The following link appears to be the related bug report for the
behavior you describe:
https://bugzilla.mozilla.org/show_bug.cgi?id=538892

it has worked fine before... I tried to open hotmail with seamonkey, and it
took ages to load a page but I think perhaps that was hotmails fault.