Praise be to Allah.
The free woman who has attained the age of majority is obliged to cover her entire body during prayer, apart from her face and hands, because all of her is ‘awrah. If she prays and any part of her ‘awrah becomes uncovered, such as a shin or foot or all or part of her head, then her prayer is invalid, because the Prophet said:
"Allaah will not accept the prayer of a woman who has started to menstruate, except with a khimaar (covering)" (Reported by Ahmad, Abu Dawud, Ibn Maajah and al-Tirmidhi, with a saheeh isnaad)
Abu Dawud reported from Umm Salamah (may Allaah be pleased with her) that she asked the Prophet (peace and blessings be upon him) about a woman who prayed wearing a dir’ (chemise or upper garment) and a khimaar (head cover), but no izaar (lower garment). He said: "The woman is ‘awrah."
As for the face, the Sunnah is to uncover it during prayer, so long as no non-mahram men are present. According to the majority of scholars, the feet must be covered; some scholars allow uncovering the feet but the majority say the opposite. Abu Dawud reported from Umm Salamah (may Allaah be pleased with her) that she was asked about a woman who prayed in a khimaar and qamees (dress or gown). She said, "There is nothing wrong with it if the dir’ (chemise) covers her feet." In any case, it is better to cover the feet, to be on the safe side. As far as the hands are concerned, there is more leeway: there is nothing wrong with either covering them or uncovering them, although some scholars think that it is better to cover them. And Allaah is the Source of strength.