Outlook express is a windows application not a web service, you may mean Outlook Web Access, which is a web based service. This you can open with any browser on Mac, though you get the older version without drag and drop on all platforms except windows IE,
If you need a fully functioning mail client that supports MS exchange servers, buy Office 2008 for Mac - though you must buy the full version not the Home/student version to get the exchnage support. If you don't need the added bells and whistles of exchnage, just POP/IMAP access then you can access you account using the Mail application included with OS X.
Alternatively you can run Outlook Express through a virtualisation system like Parallels, VirtualBox (free) or VMware Fusion but then you need to install Windows within OSX.
Lastly, when you say 'add to your mobile me account' I am slightly confused. Mobile Me is a service form Apple that comes with an email account of its own. I guess you could forward your existing mail account to it. If you mean to add the account to the mail program on OS X , called Mail or sometimes Mail.app, then as I said, yes you can. To get the settings to do so you would have to ask your ISP or sysadmin.
