Nope. And they don't need a court order either. When you sign up to a Hotmail account, you accept the terms and conditions. Read them closely
From the link:
Frank said in his statement that no court order was needed to conduct the searches.
“Courts do not issue orders authorizing someone to search themselves,” he said. “Even when we have probable cause, it’s not feasible to ask a court to order us to search ourselves.”
Hotmail’s terms of service includes a section that says, “We may access or disclose information about you, including the content of your communications, in order to … protect the rights or property of Microsoft or our customers.”