It is safe if you are aware that any content you see or provide
- may be seen by other people
- may be manipulated on the way
It does not matter if the site is run by a trustworthy party or not. SSL is used to protect the transmission of data packets on their way through untrusted networks.
Certificates are used to verify the identity of the server. This is required to prevent man in the middle attacks. Otherwise an attacker could claim that he is the real server and your browser would happily send encrypt messages encrypted for the private key of the attacker.
PS: SSL does have the issue that some certification authorities such as VeriSign, Commodo and DigiNotar have issued certificates to wrong people in the past. Only the last one was distrusted by the common browsers. But this is another topic.