Don\'t know much about encryption...
Say I\'m preparing a SAML request to submit to an identity provider. Why would I need to apply an x.509 certificate to this request?
In practice, you could use HTTPS (SSL/TLS) to protect your SAML message. But you would want to use two-way SSL certificate verification/validation, meaning your client would need to verify the server's X.509 certificate and the server would need to be configured to perform client authentication, which would require it to check an X.509 certificate that the client presents. So, the client would need its own certificate anyway.
SSL/TLS is not really designed for this...it was/is designed to protect web traffic from being seen while in transport and for the client to be able to tell what server they are talking to and sending sensitive information to (it was really designed for e-commerce where the client (user buying something) knows who they are sending their credit card information to). In the case of SAML, the whole point is for the parties to know that the information they are exchanging has not been altered in transport and that each is talking to who they think they are. Using certificates to sign/encrypt that message itself accomplishes that.