A firewall makes life a bit harder for anyone trying to hack your personal computer. Personally I wouldn't worry too much about that, as you're highly unlikely to have anything on your PC that any hacker worth his salt would care about, and any hacker not worth his salt isn't worth caring about yourself.
However, hotmail is a website run by microsoft on servers in america.. they have many, many measures to prevent their servers being hacked, but it's p*** easy to hack an account stored on their servers. Remember when you signed up and gave them a secret question to ask in case you ever forget your password? "Pet's name?" for example.. think how many people know the name of your pet and you'll understand why it's easy for people to get into your account. The kind of people who do that are utter tossers, and certainly aren't to be thought of as hackers as they have as much hacking skill as a 5 week dead trout, but that doesn't stop them making life hell for the sake of a bit of strangely twisted fun...
If you want your email to actually be safe, either you want to get your email through a POP email system (you've probably got an email address like '
[email protected]' which you download into outlook express or similar), or save a copy of any important emails onto your computer instead of just leaving them sitting on the hotmail website.