The regular free hotmail service is web based email and can't be accessed on the iPhone like POP and IMAP. You can either check it using Safari or pay for the premium hotmail service which I think is about $20 a year.
I have had issues logging into hotmail the traditional way. If you use Microsoft mobile login, it will be a successful login each time through Safari. You can simply maintain an open hotmail page on Safari for easy access and checking. You won't be able to set Hotmail up as an email account on your phone. Just access it via the web through MSN Mobile. http://mobile.live.com.