Were the carnal Corinthians that Paul wrote to actually saved believers?

Yes. Paul addresses them as carnal, fleshly babes, yet declares they are in Christ and in the Body of Christ, having been baptized into the Body and made to drink into one Spirit. They were believers who were carnal and had a long way to go, not unsaved people.

Les explains that Paul is not picking out just a few more spiritual Corinthians; he addresses all of them. He calls them carnal, fleshly, even babes, but asks where these babies are—in Christ. Les stresses that it is easy to say these people were not believers, but 'Oh yes they were.' They were in the Body of Christ, yet carnal, with a long way to go. Their carnality led to questions about marriage and meat offered to idols, which Paul had to address.

1 Corinthians 3:1

And I, brethren, could not speak unto you as unto spiritual, but as unto carnal, even as unto babes in Christ.

Who is Paul referring to when he calls the Corinthians 'carnal'?

Paul is referring to saved believers in Christ who remain fleshly minded. They have been born again and placed into the Body of Christ, but they are still controlled by the Old Adam rather than the Holy Spirit. Spiritually weak, they are babes needing milk, not solid food.