Are the face and hands 'awrah?
There is difference among the madhabs on whether a woman's face and hands are 'awrah in front of a non-mahram male. Some consider them to be part of 'awrah and some do not. Some madhabs do not originally consider them to be 'awrah but consider it necessary for young women to cover them because of the greater risk of fitnah in modern times. Some madhabs hold that they are not 'awrah but say that it is still haram for a male to look at them.
Each group bases its view on what it considers to be valid evidence and makes an alternate interpretation for the evidence of the opposing group. For example they may give precedence to an alternate tafsir, or may say that a text makes it recommended not obligatory, or they may explain a text to be abrogated or specific to certain circumstances etc.
Evidence for the stance that they are not 'awrah:
One opinion is that the face and hands are not awrah, so it is not obligatory on the woman to cover them - as long as there is no desire or risk of fitnah.
The evidence for this view includes one interpretation of the Quranic verse:
ولا يبدين زينتهن إلا ما ظهر منها
And to not expose their adornment except that which [necessarily] appears thereof
— Quran 24:31
As Tafsir traditions are recorded from Aisha, Ibn Abbas and others from among the sahaba and tabieen that the exception here essentially means the face and hands. See Tafsir al-Tabary.
Further the evidence of this view includes the explicit hadith:
إن المرأة إذا بلغت المحيض لم تصلح أن يرى منها إلا هذا وهذا . وأشار إلى وجهه وكفيه
When a woman reaches the age of menstruation, it does not suit her that she displays her parts of body except this and this, and he pointed to his face and hands.
— Abu Dawud
Further it is supported by the following ahadith:
أومت امرأة من وراء ستر بيدها كتاب إلى رسول الله صلى الله عليه وسلم فقبض النبي صلى الله عليه وسلم يده فقال " ما أدري أيد رجل أم يد امرأة " . قالت بل امرأة . قال " لو كنت امرأة لغيرت أظفارك " . يعني بالحناء .
A woman made a sign from behind a curtain to indicate that she had a letter for the Messenger of Allah (ﷺ). The Prophet (ﷺ) closed his hand, saying: I do not know this is a man's or a woman's hand. She said: No, a woman. He said: If you were a woman, you would make a difference to your nails, meaning with henna.
— Abu Dawud
كان الفضل رديف النبي صلى الله عليه وسلم فجاءت امرأة من خثعم، فجعل الفضل ينظر إليها، وتنظر إليه فجعل النبي صلى الله عليه وسلم يصرف وجه الفضل إلى الشق الآخر
Al-Fadl was riding behind the Prophet (ﷺ) and a woman from the tribe of Khath'am came up. Al-Fadl started looking at her and she looked at him. The Prophet (ﷺ) turned Al-Fadl's face to the other side.
— Bukhari
أن امرأة، جاءت رسول الله صلى الله عليه وسلم فقالت يا رسول الله جئت لأهب لك نفسي. فنظر إليها رسول الله صلى الله عليه وسلم فصعد النظر إليها وصوبه، ثم طأطأ رأسه
A woman came to the Messenger of Allah (ﷺ) and said: 'O Messenger of Allah (ﷺ), I have come to give myself to you (in marriage).' The Messenger of Allah (s.a.w) looked her carefully, then lowered his head.
— Bukhari
In these incidents it is apparent that the women had their face or hand uncovered and the Prophet ﷺ did not condemn them for doing that.
It is also considered permissible because of necessity, as habitually these parts are uncovered when dealing with people and there is hardship in keeping them covered. And there are also other reports which support this opinion.
Evidence for the stance that they are 'awrah:
The second madhab is that the entire body of a woman is 'awrah in front of a non-mahram male. Hence the face and hands are 'awrah too. This is based on the alternate interpretation of the Quranic verse:
ولا يبدين زينتهن إلا ما ظهر منها
And to not expose their adornment except that which [necessarily] appears thereof
— Quran 24:31
As tafsir traditions are recorded from Ibn Masu'd that the exception here means clothing only. See Tafsir al-Tabary.
It is also supported by the following verse:
يا أيها النبي قل لأزواجك وبناتك ونساء المؤمنين يدنين عليهن من جلابيبهن ذلك أدنى أن يعرفن فلا يؤذين وكان الله غفورا رحيما
O Prophet, tell your wives and your daughters and the women of the believers to bring down over themselves [part] of their outer garments.
— Quran 33:59
As the apparent meaning of this verse is to cover everything, and no exception is mentioned. It is even explicitly narrated from some of the salaf that this means that a woman should cover everything, see Tafsir al-Tabary.
Similarly it is supported by the apparent meaning of the following verse:
فاسألوهن من وراء حجاب ذلكم أطهر لقلوبكم وقلوبهنا
When you ask for something, ask them from behind a partition. That is purer for your hearts and their hearts.
— Quran 33:53
As it commands keeping a veil between two individuals and does not make any exception for the face or hands.
Does the hadith المرأة عورة support the second view?
The hadith is open to interpretation. Even if we extend it to clothing it does not explicitly forbid uncovering the face and hands and it can be argued that other texts and evidences should be combined with it to know some exceptions.
However this hadith has been used as evidence by some of the scholars supporting the second opinion. For example islamweb lists this hadith among the evidence for the face veil:
روى الترمذي وغيره من حديث أبي هريرة أن النبي صلى الله عليه وسلم قال : " المرأة عورة فإذا خرجت استشرفها الشيطان ". وهذا دليل على أن جميع بدن المرأة عورة بالنسبة للنظر
Tirmidhi and others have narrated the hadith that The Messenger of Allah ﷺ said: 'Woman is ‘awrah (that which must be concealed), and when she goes out the Shaytaan’s hopes are raised.'
And this is evidence that the whole body of a woman is 'awrah with respect to looking
— islamweb.net
Similarly, Ibn Qudamah records the use of this hadith by some scholars as the base case for the 'awrah of a woman:
وقال بعض أصحابنا: المرأة كلها عورة؛ لأنه قد روي في حديث عن النبي - صلى الله عليه وسلم -: «المرأة عورة» . رواه الترمذي، وقال: حديث حسن صحيح. ولكن رخص لها في كشف وجهها وكفيها؛ لما في تغطيته من المشقة، وأبيح النظر إليه لأجل الخطبة؛ لأنه مجمع المحاسن. وهذا قول أبي بكر الحارث بن هشام قال: المرأة كلها عورة حتى ظفرها.
— Al-Mughni
