Allah says in the most Holy Quran "And Say to the believing women to lower their gaze (from looking at forbidden things), and guard their modesty".
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.
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.