Good day Matt,
My responses below your questions.
Assuming your organization is tracking weather patterns fairly regularly, how are you doing so?
For the utilities I worked with The Transmission System Control Centers that would track the weather.
Specifically, where in your workforce hierarchy is weather tracking?
It has been the system dispatcher in the Control Center who would be responsible for tracking the weather.
Do you have an employee or whole department who's tracking upcoming weather patterns and feeding that information to those who need it (planning for demand, emergency response, etc.)?
It was generally left up to the folks in the control room.
What tools do they use to do so?
Some control centers use Pelmorex's weather service, Storm Tracker and some used Indji software that monitors information on natural hazards like fires, lightning and severe weather in real-time and compares the location and nature of this information against your actual infrastructure.