If you'd like linguistically rigorous names, you might consider the meanings of
-mancy and
-urgy, which come from Greek.
-mancy has to do with divination (a necromancer is someone who speaks with and learns things about the dead), and
-urgy is about doing work. This was addressed in an old post:
http://forums.sjgames.com/showthread.php?t=28658
So divining things about air, earth, fire, and water would be aeromancy, geomancy, pyromancy, and hydromancy (not
aqua-, that's Latin, not Greek), and their practitioners would be aeromancer, geomancer, pyromancer, and hydromancer. Creating, changing, and destroying these elements would be aerourgy, geourgy, pyrourgy, and hydrourgy (or maybe aerurgy, geurgy, pyrurgy, and hydrurgy; I'm not sure how the roots combine), and their practitioners would be aerourgist, geourgist, pyrourgist, and hydrourgist (or aerurgist, geurgist, pyrurgist, and hydrurgist).
You can extend this to many of the other colleges too, if you know the Greek roots for those words. Necromancy is divination of spirits and the dead; necrourgy/necrurgy would be summoning, controlling, and destroying spirits and the dead.
If you're sticking with English, a good word for weather spells is weatherworker.