Is it permissible for a pilgrim in the state of Ihram to cover his feet while sleeping during intense cold during the Hajj rituals?

There is no harm for a male pilgrim (muhrim) performing Hajj or Umrah (definition) to cover his foot with a cloth, such as his Rida' (upper garment) or Izar (lower garment). This is because what is prohibited is tailored clothing that fits the limb, such as socks. This is based on the Prophet's (peace and blessings be upon him) saying: "Do not wear shirts, turbans, trousers, burnooses, or khuffs (leather slippers), except for one who cannot find sandals, then let him wear the khuffs and cut them below the ankles." As for women, it is permissible for them to cover their entire body with any covering except their face.