Is what is narrated about the Prophet, may God’s prayers and peace be upon him and his family, true, concerning the prohibition of sleeping with windows open in autumn due to the harm it entails?

There is no prophetic hadith (definition) that states what was mentioned, nor has it been found in the books of Sunnah (definition), or weak and fabricated hadiths. The only exception is what Al-Ajlouni mentioned regarding a widespread hadith: "Guard yourselves against the cold of autumn, for it causes disease in your bodies," about which he said: "I do not know it to be a hadith, let alone its authenticity."