Question:
Do women have to wear head coverings when praying in private?

Answer:
We have instruction regarding head coverings in 1 Corinthians 11:1-16, where we learn about the headship, or positions of authority, that God has established in creation. The book of Corinthians is full of teaching concerning the assembly God’s people. In fact, the portion that immediately follows verse 16 in chapter 11 directly addresses one of the assembly meetings. Therefore, we can be certain that the instruction regarding wearing head coverings should be carried out when there is praying or prophesying in public meetings of the assembly.

Now in direct response to the question, we are not given specific instruction regarding the wearing of head coverings in times of private prayer, only in the public realm of assembly gatherings. Since God has not given us clear instruction regarding the wearing of head coverings during private prayer, this matter must be one that the Lord wants us to decide on an individual basis.
Some women believe that they should wear head coverings when praying in private since the truth of headship still exists even when no man is present. They want to continue to express their God-given place in His order of headship since they know that the angels are still watching them, even when no one else is present (1 Corinthians 11:10). However, other women believe that God can see their desire to be in their proper position in God’s order of headship and so do not need to outwardly express this belief by wearing a head covering when they are privately praying.Therefore, since Scripture does not directly address the wearing of head coverings while in private prayer, God will show His will regarding this matter to all who desire to do that will (John 7:17). May our desire be to do all to the glory of God in this particular matter.