Hence a woman has been instructed to put on a head-covering when she prays. As for her face, hands, and feet1, she is only forbidden to expose them to unrelated men; she is not prohibited from showing them to other women or to her close male relatives. This makes it clear that they are not of the same category as the parts a man must conceal from other men, or a woman from other women—those areas whose exposure is prohibited because of the obscenity and ugliness involved in uncovering them. Rather, this matter concerns the preliminaries that may lead to indecency, so the ban on exposing them is intended to block the road to such indecency, as He said:
“That is purer for them.”2
And in the verse of the veil He said:
“That is purer for your hearts and theirs.”3
Thus He forbade this as a preventative measure, not because these parts constitute absolute nakedness, whether in prayer or outside it. That being clarified,

To obligate a woman to cover her hands in prayer is highly unlikely, for the hands prostrate just as the face prostrates4. In the Prophet’s time the women possessed only simple tunics; they engaged in their daily tasks while wearing those tunics, and would bare their hands when kneading dough, grinding grain, or baking bread. Had covering the hands during prayer been obligatory, the Prophet ﷺ would certainly have made it plain—and the same applies to the feet. What he actually commanded was only the head-covering together with the tunic, so the women used to pray in their tunics and head-coverings.