Does a woman's uncovering of her face during Hajj and Umrah indicate that her face is not 'awrah (private parts that must be covered)?

It is not correct to infer from the prohibition of the female pilgrim (muhrimah) from wearing the niqab that her face is not awrah (private part). The prohibition is not about covering the face entirely, but rather specifically about wearing the niqab. She is permitted to cover her face with something other than the niqab, such as the sidāl (a large veil) or the ṭarḥah (a head covering). This is supported by the actions of the female Companions, who used to cover their faces with something other than the niqab when men passed by. The face of a woman in ihrām is like the body of a man in ihrām: it is forbidden to cover it with something tailored to its shape, like the niqab, but not by covering the face with a khimār (headscarf) or a thobe (garment).