What is the ruling on performing ghusl for Fajr prayer when the weather is cold and water cannot be heated until after the time for prayer has passed?

The duty was to heat the water and perform ghusl with it, even if you missed the congregational prayer. If you were unable to heat the water, you should have performed tayammum and prayed. However, since you performed ghusl with cold water while in a state of janaba, you must repeat the Fajr prayer after performing ghusl.