I think you are looking for any Windows hosting that offers Exchange hosting.

I do not think there is such a thing for Outlook hosting since all Outlook is a glorified mail client.

Is this what you mean? Or am I not on the right track here?

There is an Outlook web client that can be used with exchange also. Exchange is real time to so you can access from anywhere so you can updated email and get to the same areas from an Outlook client or a web based Outlook client.