بسم الله الرحمن الرحيم
If the women come out of their homes for some need they should cover their faces as well. It is not enough to only cover their head and wear loose garments. It is mentioned in the holy Quran:
يَا أَيُّهَا النَّبِيُّ قُل لِّأَزْوَاجِكَ وَبَنَاتِكَ وَنِسَاء الْمُؤْمِنِينَ يُدْنِينَ عَلَيْهِنَّ مِن جَلَابِيبِهِنَّ …..
O Prophet, tell your wives and your daughters and the women of the believers that they should draw down their shawls over them.
The verse speaks about Jalabeeb (plural of Jilbab) which is a long chuddar. Hadhrat Ibn Masaood (رضى الله عنه) said regarding the chuddar that it was worn over scarf (Ibn Kathir), while Hadhrat Ibn Abbas (رضى الله عنه) has explained it in the following way:
أمر الله نساء المومنين إذا خرجن من بيوتهن فى حاجة أن يغطين وجوهنن من فوق رؤوسهن بالجلابيب ويدنين عيناً واحدةً .
Almighty Allah has ordered Muslim women that if they come out of their homes for any need they should draw down their shawls and cover their faces and keep only one eye open (to see the way).
Imam Muhammad Seereen says that he asked Hadhrat Ubaidah Salmani the meaning of this ayat and asked the nature of Jilbab then he draw down his shawl from head and covered his face and kept his left eye open and explained it practically. (Maarif al-Quran 7:223) By the said tafsir, the ruling of hijab of face was learnt clearly.
Allah knows Best!
Darul Uloom Deoband