From The Textual Proof For The Obligation Of The Niqaab, Part 2, By Ibn ‘Uthaymeen
“Male riders would pass by us while we (wives) were in the state of ihraam with the messenger of Allaah. When they would approach us, (each) one of us would let her jilbaab fall down from (the top of) her head over her face. And when they had passed on, we would uncover our faces.” [Ahmad, Aboo Daawood and Ibn Maajah]
Ibn ‘Uthaymeen comments:
“In her statement: “When they (male riders) would approach us, (each) one of us would let her jilbaab fall down from (the top of) her head over her face” is a proof for the obligation of covering the face. this is because when one is in the state of ihraam, it is obligatory to uncover the face. So if it were not for the strong restriction against exposing the face, it would have been obligatory for them (i.e. the Prophet’s wives) to remain uncovered, even in the presence of the male riders.(1)
To clarify this point further: Uncovering the face in the state of ihraam is obligatory on all women, according to the majority of scholars. And the obligatory act does not get overridden, except by something else that is obligatory (to a stronger degree). Therefore, if veiling the face in front of make strangers were not obligatory, it would not have been permitted to abandon the obligatory act of exposing the face in the state of ihraam.
Shaykh Al-Islaam Ibn Taymiyyah said: ‘This hadeeth is from that which shows us that the face veil (niqaab) and the gloves were widely known to women who were not in ihraam. This is evidence for the covering of their faces and hands.’ “
(1) What the shaykh means here is that those in ihraam are obligated to uncover their faces, however ‘Aa’ishah would cover her face in the presence of male riders, so it is only obvious to assume that there is a stronger obligation overriding this obligation (of those in ihraam uncvoering their faces). So even though someone in ihraam must uncover their face, the obligation of a woman covering her face is an even stronger obligation.
[Taken from “Four Essays On The Obligation Of Veiling” Ch. 2: An Essay On Hijaab, Pp. 40-41]