I can think of another story about a Roman emperor taking into account some weather omen--I want to say it was Constantine and that it had something to do with his conversion.
I'm curious about any additional examples which people can cook up.
Almost every source I use to look up on the Mongol invasion of Japan claim that convenient occurrences of typhoons... written by u/ParallelPain discusses the Mongol invasion and the role of weather (or lack thereof).
Depending on your definition of "change history" How did storms affect medieval battles? ... written by u/Imperial_Affectation discusses a battle in which the weather played a role