I live in the US. In the city of my residence, we sometimes experience extreme winter weather conditions. Considering this, would it be permissible to cancel or postpone the Friday prayer if it coincides with one of these days? Kindly provide me with textual proofs.

There is a consensus among jurists on the permissibility of refraining from attending congregational prayers at mosques due to severe rain, floods, snow, or wind among other matters that pose danger to the safety of people or place hardship on them. Nafi’ reported that Ibn Umar once pronounced the call to prayer on a cold and stormy night and said, “Pray in your homes.” Then he said, “Verily, the Messenger of God (peace and blessings be upon him) would order the caller to prayer to say on a cold or rainy night: ‘Pray in your homes’” (Sahih Bukhari).

Another textual evidence was reported by Anas Ibn Malik. He narrated that a blind man, ‘Utban Ibn Malik, told the Prophet (peace and blessings be upon him), “O Messenger of God! It sometimes gets dark and floodwater flows [into the valley]. I am a man of poor eyesight so please pray at a place in my house that I might take it as a place of prayer.” So the Messenger of God (peace and blessings be upon him) went to the man’s house and said, “Where would you like me to pray?” The man pointed to a place and the Messenger of God offered the prayer there” (Sahih Bukhari).

Therefore, any extreme weather conditions you may experience permit you to refrain from going to the mosque for the Friday and congregational prayers. You may pray at your home instead and pray the Friday prayer as the noon prayer with four rak’as.
And God Almighty knows best.