It should be noted that just as the face veil is obligatory in normal circumstances, it is also obligatory in the state of Ihram. However, the veil should be worn in such a way that the cloth does not touch the face.
In the state of Ihram, it is necessary to follow both rulings (keeping the face covered as well as ensuring the cloth doesn’t touch the face) simultaneously, which is possible and has been practiced since the time of the Sahabyaat. Hazrat Aishah (may Allah be pleased with her) mentioned that when they were traveling on camels for Hajj, they would turn their niqabs (face veils) back when there were no ghair-mahram men around on the road. They would also have a piece of wood attached to their foreheads. When they saw a caravan or a ghair-mahram man approaching, they would lower their niqabs onto the wood, preventing it from touching their faces while also keeping their faces hidden from the approaching man.
Mulla Ali Qari (Rahimahullah) writes in the tashreeh of this hadith in his book مرقاۃ (Marqah – the renowned tashreeh of the book of Hadith Mishkat) that the face was veiled in such a way that the cloth did not touch the skin of the face.
In essence, both of these rulings should be followed simultaneously. This can be achieved by adopting a method of veiling the face that is both convenient and ensures that the cloth does not touch the skin. For instance, a hat with a cloth is attached to its brim to cover the face can be worn, or a normal veil can be worn in a way that it does not touch the face.