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Jim, even with a private e-mail system, such as the one we have at work, we tell users in the Acceptable Use Policy that anything they send on it is to be for business use, and is the property of the agency. As a former IT director for a K-12 school district, we had similar language there as well.
Regardless, once you "send it out", there is always the possibility that it can be intercepted and read by those other than the intended recipient.
CAN they do this? Sure. Is it ethical? Maybe, maybe not. I have not read the T's and C's from Hotmail since I created my account in 1989. I am sure they have changed since then. I would certainly be surprised if their agreement did not give them the ultimate right to do that. The agreements are usually written for the protection of the company, not the user.
Bottom line, I would personally not send anything out on a public network like that, that I was not willing to have made public...