"Should sisters wear hats—head coverings—when we come together in a private home for a special meeting, perhaps informal in character?"
ANSWER: For the general principles of women's head covering we refer you to a pamphlet entitled, "Because of the Angels," which is for sale by the publishers. The Spirit of God has laid down certain rules in 1 Corinthians 11, and has also explained that the angels are spectators of things on earth. They should be able to witness in the Church on earth God's order of headship by seeing the man "uncovered" and the woman "covered" at the time of prayer; but alas! it is generally disregarded in Christendom, and so disorder and confusion are to be witnessed by the heavenly intelligences. The lack of adherence to the rules, however, is no reason why any of us should be guilty of the same thing. We have the Word of God to guide us.
In answer to your specific question regarding proper order in special meetings held in private homes, we would ask a few questions. Are the brothers and sisters, or even sisters only, invited to come together for the purpose of having certain questions concerning the Scriptures discussed? or perhaps to hear some brother give a talk on the Scriptures? If the answer is "yes" in either case, then is it not proper that such a meeting should begin and end with prayer? Can we think of not seeking the Lord's guidance and help at the beginning of such a meeting, or of not turning to Him in thankfulness at its close? Then in such instances the sisters are there in the place where prayer is wont to be made, and certainly should have a covering on their heads. The fact of its being a special or extra meeting, or of its being held in a private home, does not alter that. The heads of sisters should be covered, and the heads of brothers uncovered, in such meetings.
There may be cases where you may invite a few brothers and sisters to your home for dinner, and after the meal the conversation naturally turns to the Word of God, and perhaps a chapter is read; this is somewhat different than a called meeting and becomes more of a family discussion of the Scriptures; but even then, if prayer is made, each sister by all means should place a handkerchief or some other covering over her head at the time of prayer. There should not be a question about this, for she should so act in the privacy of her own home. It is a matter of godly order to be witnessed by heaven even though no other human being is there to see.
Whenever a sister is in the attitude of prayer, whether actually speaking to God herself, or where another is doing so, she should be covered, as the sign of submission to God's constituted authority. The same rule would apply for a man having his head uncovered. The only modification of the application of this important part of the Holy Scriptures would be when one is not in the attitude of prayer; for instance, one may pass out a tract on a street or in a public conveyance and at the same time silently ask the Lord to bless the printed word; or, one may at any time lift the heart to the Lord for His guidance and help without getting into an attitude of prayer. How quickly one may in spirit desire, "Lord, guide me," or "Lord, help me."
We desire for ourselves, and for all the dear saints of God, a greater simplicity about the Scriptures, that will accept things without reasoning, and also a deeper reverence for and trembling at the Word of God, and the spirit of subjection of heart and mind to its divine precepts.