尝试一下:

Conversation.findOne({
    _id: conversation_id
}, function(err, docs) {
    if(err) return next(err);
    if(docs)
    {
        docs.messages.forEach(function(msg,index,array)
        {
            msg.deleted_by.push(req.loggedInUser._id);
        });
        docs.save();
    }
});

阅读此以取得更好的效果了解forEach函数.

Read this for better understanding of forEach function.

我希望这会有所帮助.