Scholars outside the four schools
Ibnu Ḥazm holds the face is not ʿawrah; Ibnu Taymiyyah holds the permissive evidence abrogated. Both arguments turn on the same body of reports, read in opposite directions.
Ibnu Ḥazm and the Ẓāhirī school
Ibnu Ḥazm holds that the face and hands are not ʿawrah and that covering the face is not obligatory. He argues from the ḥadīth of al-Faḍl b. ʿAbbās, who gazed at a beautiful woman in the Prophet's presence without the woman being instructed to cover, and permits uncovering even where a woman is beautiful and looked at with desire.
Whether this is the Ẓāhirī school's position or his own cannot be established. The reason is concrete rather than evasive: the school's surviving sources are very limited, and the only complete work of the school to reach us is al-Muḥallā — which is Ibnu Ḥazm's own.
Note also that non-obligation is not rejection. Holding something not required is not holding it illegitimate.
Ibnu Taymiyyah and Ibnu al-Qayyim
Both hold covering obligatory. Ibnu Taymiyyah's argument is abrogation: the verses and reports permitting a woman to show face and hands belong to an earlier period, and were abrogated by the jilbāb verse. After that, on his view, a woman may not show face, hands or feet to unrelated men. He includes the face in the "inward adornment" of al-Nūr 24:31.
Set beside Ibnu Ḥazm, the shape of the disagreement becomes clear: both are working from the same reports. One reads the permissive material as still operative; the other reads it as superseded. The dispute is not about which texts exist.
Others
Isḥāq b. Rāhawayh recommends niqab for a woman of beauty without requiring it. Abū Manṣūr al-Māturīdī holds that for a young woman, covering the face and hands is the better and more excellent course, not because uncovering is forbidden, but for fear of arousing desire. He is argued to have never finalised the matter: elsewhere he is read as using the language of obligation for a young woman who is attractive, which is said to cast further doubt on treating him as a clean non-obligation view. Al-Shaʿrānī, al-Maqbilī and al-Ṣanʿānī all treat the face as covered from strangers — al-Ṣanʿānī adding that even in iḥrām what is prohibited is the niqab-garment, not covering as such.
Al-Shawkānī on a false attribution
Al-Mahdī Aḥmad b. Yaḥyā b. al-Murtaḍā, in al-Baḥr, attributed to all four imams — Abū Ḥanīfah, Mālik, al-Shāfiʿī and Aḥmad — the position that a man may look at an unrelated woman's face.
Al-Shawkānī rejects the attribution as bāṭil, and argues from Qurʾān and sunnah in the opposite direction.
This is worth keeping in view. Attributions to the four imams on this question are made confidently in both directions, and this site has already recorded the finding that their actual positions cannot be determined.
Check your understanding
Ibnu Ḥazm (face not ʿawrah, not obligatory) and Ibnu Taymiyyah (face covering obligatory via abrogation) reach opposite conclusions. What does the note say about their arguments?