Absolutley NOT unless the information in your messages and contacts is already in the public domain!
Don't get me wrong - OWA provides an excellent webmail system.
My point is that if you don't have a reason to trust the client machine you shouldn't view/access or enter sensitive information as anything you see/type can be stolen by a malicious third party. Using multi-factor authentication (aka "blinkin' tokens"), HTTPS/SSL on protects the transport (and authentication of the parties).
I am staggered at the number of organisations who allow (and encourage) their employees to access corporate information from unmanaged machines!!!!
There ARE cyber cafes who are very good at ensuring the security of the client machine - it's a differentiator - however the VAST majority of cyber cafes do not provide this assurance