Unfortunately, I can sense storm fronts as they approach. Very violent systems, especially those that have the capability to form tornadoes really stand out. The weather shifts kick off migraines.
When I was younger, I could feel them, and they mainly just made me nervous, as I got older, the migraines started. On really bad ones, 350+ miles is about when I start feeling them. At half that distance, I just about lose vision in one eye. Hurricanes are the worst, followed by tightly wrapped low pressure systems with a long, powerful trailing cold front.
Yes, I firmly believe some animals are very sensitive to weather, and natural selection has enhanced their abilities to use it to their advantage.