I say, and with God's success: The condition of cold that permits performing tayammum instead of ghusl (full ablution) is when one fears illness from using cold water, or the loss of a limb, or death, whether one is a resident or a traveler. Tayammum due to cold is specific to ghusl and not to wudu (partial ablution) according to the correct view. This often occurs outside urban areas, as heating water at home is possible, and it may be in urban areas but one cannot find a way to heat the water, so he may perform tayammum in this case; because the lack of water and warmth, even if rare, does not contradict the permissibility of tayammum. It was narrated from Amr ibn al-Aas (may Allah be pleased with him): "I had a wet dream on a cold night during the battle of 'Dhat al-Salasil', and I feared that if I bathed, I would perish, so I performed tayammum and then prayed Fajr with my companions. They mentioned this to the Prophet (peace be upon him), and he said: 'O Amr, did you pray with your companions while you were in a state of janabah (impurity)?' I informed him of what prevented me from bathing, hoping that I heard Allah say: {And do not kill yourselves} (An-Nisa: 29), and the Messenger of Allah (peace be upon him) laughed." This is found in Al-Mustadrak 1: 285, Al-Sunan Al-Sughra 1: 185, Al-Sunan Al-Bayhaqi Al-Kabir 1: 225, Al-Sunan Al-Daraqutni 1: 178, Al-Sunan Abu Dawood 1: 92, and Musnad Ahmad 4: 203. See: Fath Bab Al-'Inayah 1: 110, and Allah knows best.