The problem is that only the body is encrypted. Who you are communicating with (and in term, who they are communicating with) is at least as sensitive as what you are writing.
If they're wiretapping everything, there's no way for you to hide the fact of a communication taking place, but at least you can protect the data itself using client-side encryption.
No, you misunderstand. With S/MIME, the email headers are not encrypted. This means someone can go to your email provider, get all your emails, and even though these are all S/MIME encrypted, build a nice graph of who you are communicating with, how often, correlate with significant dates, see the subject of each letter, file names of attached files, etc.
To make life tougher on spies, add fake email messages to the pool regularly.