Hotmail does not have an IMAP option for desktops, unless you are running Windows Live Messenger which is Windows only.
I'm not familiar with mBox Mail but I note on their site that they do not seem to be in any hurry to fix the problem with Mountain Lion.
There are a lot of people asking the same question as yourself.
Personally, I would go with Gmail over Hotmail, Microsoft has done nothing but make it very difficult for Mac users to use Hotmail.
I have a MacBook Pro running Mac OS X 10.8 Mountain Lion. When I go the computer it was running Lion and i purchased mBox Mail as a go through for my Hotmaill.com accounts so I could have access to my email folders within the Mac Mail program. Since moving to Mountain Lion mBox Mail has not been updated and my email is back to being read as a POP3 account. I contacted the mBox manufacturer for a solution, but the work around they provided does not work at all. Does anyone know what I can do to get IMAP functionality back to Mac Mail? I have thought about switching to gmail, but am still skeptical at this time. I have MS Office for Mac 2011 and would like to go back to using Outlook. Is there a way to get Outlook to read my existing email as IMAP and not POP3?