Paul mentions sons of disobedience in one other epistle, namely Ephesians.
And you were dead in the trespasses and sins in which you once walked, following the course of this world, following the prince of the power of the air, the spirit that is now at work in the sons of disobedience—among whom we all once lived in the passions of our flesh, carrying out the desires of the body and the mind, and were by nature children of wrath, like the rest of mankind. But God, being rich in mercy, because of the great love with which he loved us, even when we were dead in our trespasses, made us alive together with Christ—by grace you have been saved...
(Ephesians 2:1-5 ESV)
In this passage, sons of disobedience is connected to believers before they were saved. It speaks about man's nature before he is born again/regenerated.
Here is the some of the context of Colossians 3:6
Put to death therefore what is earthly in you: sexual immorality, impurity, passion, evil desire, and covetousness, which is idolatry. On account of these the wrath of God is coming. In these you too once walked, when you were living in them. (Colossians 3:5-7 ESV)
This passage is actually very similar to Ephesians 2 because it talks about the sinfulness of the audience before coming to Christ.
Whoever believes in the Son has eternal life; whoever does not obey the Son shall not see life, but the wrath of God remains on him. (John 3:36 ESV)
The wrath of God is for those (sons of disobedience) who have disobeyed God and broken his law. Faith in Jesus Christ saves such people from the wrath of God.
"Sons of disobedience" is a title given only to non-believers in the Bible, although it is possible for believers to also disobey God. However, believers do not experience the wrath of God, but they do experience God's discipline when they sin.
For God has not destined us for wrath, but to obtain salvation through our Lord Jesus Christ... (1 Thessalonians 5:9 ESV)
And have you forgotten the exhortation that addresses you as sons?
“My son, do not regard lightly the discipline of the Lord,
nor be weary when reproved by him.
For the Lord disciplines the one he loves,
and chastises every son whom he receives.”
It is for discipline that you have to endure. God is treating you as sons. For what son is there whom his father does not discipline? If you are left without discipline, in which all have participated, then you are illegitimate children and not sons. Besides this, we have had earthly fathers who disciplined us and we respected them. Shall we not much more be subject to the Father of spirits and live? For they disciplined us for a short time as it seemed best to them, but he disciplines us for our good, that we may share his holiness. For the moment all discipline seems painful rather than pleasant, but later it yields the peaceful fruit of righteousness to those who have been trained by it.
(Hebrews 12:5-11 ESV)
God's discipline is out of love for believers, who are considered his children. His wrath is associated only with non-believers, who are called the sons of disobedience.