Need to hide audit trail/history for not login users. But it should visible to login user.
It get hide after making entry in MediaWiki:Common.css file.
#ca-history { display:none!important; }
As per requirement it should remain available for user who has logined.
Your first step is correct: Make the history invisible to all users. The next step is to show it to all registered users by creating the MediaWiki:Group-user.css page with the following rule:
#ca-history {
display: block !important;
}