'Mail' is for exchange/POP/IMAP accounts. You can set up a Hotmail account this way, but you'd need to be POP/IMAP based.
The likelihood is, you're not. You can only access your hotmail account via a Hotmail app or by using the Internet, and then to log in. They may have a WAP based site which you should store in Bookmarks and then go there that way.
The phone is Android, thus it has a Google bias, hence the gmail icon as standard and not one for Hotmail.
You should be able to do both your uni email (is it exchange server?) and hotmail from the Mail app. This should help with your hotmail. I can't fully remember how I did my uni email, but I found instructions on my uni library website, so maybe have a look in the IT section on yours. Otherwise just google exchange on Android.