First, you mention "mood" in your title, but the definition uses the words "a health condition or symptom." So I get the feeling that meteoropathy might be used more for joint pain and migraines than irritable moods (although one can often cause the other).
Second, you are right, meteoropathy is a little-known and little-used word. Wikipedia lists it under a more common term that might be more recognizable to some: weather pains.
That said, articles such as this one have a longer list of possible symptoms that fall under the meteorpathy umbrella, including:
migraines, headaches, dizziness, nausea, fainting, pains in the field of old injuries, rheumatic pains, and muscle aches... fatigue, irritability, mood swings, apathy, lethargy, decreased concentration, coordination and thinking, and sleep disturbances.
I can't think of a common replacement word, though I will say that I've had a few friends who have been known to say things like:
- My knee is acting up again. Rain must be coming soon.
- My back is telling me a thunderstorm is coming.
- I'm getting a headache. Makes sense, with this clouds rolling in.