You can access Windows Live Hotmail with your iPhone: use Safari, or channel Hotmail through an external service. It works, and it is clumsy.
How about an app that works just like iPhone Mail but talks to Windows Live Hotmail instead of POP and IMAP accounts? mBox Mail is that application. You can open any folder in your account and move messages freely (and in bulk to, say, mark them as such) just like in Mail. It’s a pity mBox Mail can access only one account at a time, though.
What mBox Mail does very right is gathering contacts: not only does it use and auto-complete your iPhone addresses but those from Windows Live Hotmail as well. Composing messages, then, works much like it does in Mail — in a bit less straight-forward but in a functional manner none the less. You can even attach images from Photos and save drafts in mBox Mail, though they are not synced with Windows Live Hotmail.
For incoming emails exceeding 1 MB, you are directed to Windows Live Hotmail’s web interface. Thankfully, mBox Mail lets you read and type in both portrait and landscape mode, though.