We will see how the Salaf understood this matter:
1) The opinion of the Sahaba :
Ibn Abbas (ra) is one of the most learned men of the Sahaba (Companions). Prophet Muhammad (saw) even prayed for him saying "O Allah, make him acquire a deep understanding of the religion of Islam and instruct him in the meaning and interpretation of things." He with reference to Surah An-Nur “except only that which is apparent” as Ibn Kathir narrated with a Sahih (authentic) chain of narrators, said it’s "The hand, the ring, and the face."
Abdullah Ibn Omar Ibn Al-Khattab (ra) said “the face and the two hands”.
Anas Ibn Malik (ra) said “the hand and the ring”.
Ibn Hazm said: “all of this (statements) are in the highest of accuracy.
And so are statements by Ali (ra), Aisha (ra), and other Tabi’een”.
Now you have to think who would understand these verses better than Aisha (ra) the MOST knowledgeable woman in the matters of Islam and the wife of Prophet Muhammad (saw)?
2) Scholars among the Tabi’een had many opinions on this matter :
Some said a woman should cover all of her body except the face and the hands. This is the saying of Imam Malik, Al-Hadi, Al-Qasim (in one of his narrations), and Imam Abu Hanifa (in one of his two narrations).
Some said she should cover all her body except the face, the hands, and the foot. This is the saying of Imam Abu Hanifa (in another narration), Al-Qasim, and Ath-thouri. Some said she should cover all her body except the face. This is the saying of Ibn Hanbal and Dawood.
No one said the face of a woman is loins (‘Aura) except a weak narration from Ibn Hanbal and some Shafi’i scholars!
Sa'id ibn Jubayr, 'Ata and al-Awzai have stated explicitly that the showing of the face and hands is permissible. 'Aishah (ra), Qatadah, and others have added bracelets to what may be shown of the adornments; this interpretation implies that a part of the arm may also be shown. Various scholars (such as Abu Yusuf) have allowed the exposure of the lower part of the arm up to a length varying between about four inches to one-half of the arm.
Ibn Hazm is the Imam of the Dhahiri schools (Literal schools) mentioned many accidents prove that it is not required for a woman to cover her face.
3) The opinion of late scholars :
Assuredly a woman is permitted to show her face and hands because covering them would be a hardship on her, especially if she must go out on some lawful business. For example, a widow may have to work to support her children, or a woman who is not well-off may have to help her husband in his work; had covering the face and hands been made obligatory, it would have occasioned such women hardship and distress. Al-Qurtabi says, it seems probable that, since the face and hands are customarily uncovered, and it is, moreover, required that they be uncovered during acts of worship such as Salat and Hajj, the exemption (referred to in the verses of Surah al-Nur) pertains to them.
In addition to this, we may infer from Allah's words, "Tell the believing men that they should lower their gazes", that the faces of the women of the Prophet's time were not veiled. Had the entire body including the face been covered, it would have made no sense to command them to lower their gaze, since there would have been nothing to be seen.
Narrated Aisha, Ummul Mu'minin: Asma, daughter of AbuBakr, entered upon the Apostle of Allah (swt) wearing thin clothes. The Apostle of Allah (swt) turned his attention from her. He said: O Asma', 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 her face and hands. (Narrated by Abu Dawood # 4092).
This Hadith has three authentic narrations and was correct by all Major Hadith scholars such as Albani.
Narrated 'Abdullah bin Abbas: Al-Fadl (his brother) was riding behind Allah's Apostle and a woman from the tribe of Khath'am came and Al-Fadl started looking at her and she started looking at him. The Prophet turned Al-Fadl's face to the other side. The woman said, "O Allah's Apostle! The obligation of Hajj enjoined by Allah on His devotees has become due on my father and he is old and weak, and he cannot sit firm on the Mount; may I perform Hajj on his behalf?" The Prophet replied, "Yes, you may." That happened during the Hajj-al-Wida (of the Prophet). (Narrated by Bukhari # 589, Muslim, and others).This Hadith is very authentic since it was narrated by Bukhari and Muslim. If she was covering her face then Ibn Abbas would know that she is beautiful! Also prophet (saw) did not order the girl to cover her face. This hadith was not abrogated since it happened during Hajj-al-Wida (10 AH) while the Aya of Hijab was revealed in the 5th year after the Hijra.