As I understand it, it's their types of magic that are counters to one another. *Those* are the things that repel each other, so an earth and an ice elemental wouldn't be able to combine their talents and cast spells together, because it would be like matter + antimatter (well okay, it wouldn't actually destroy the universe, but you get what I mean xD)
The wizards themselves might not have a great deal in common, but they'd be able to be in the same room, have conversations and be perfectly civil to one another. I remember one of Linnet's first threads as a Discipuli Madin was with an ice elemental, and they got along fine, so being friends wouldn't be too much of a stretch. Obviously it would depend on the personalities of the wizards concerned.
And I would assume Zima would have a great fear of being underground (ie surrounded by Earth) but would have no problem actually being in nature (where there will also be water, air etc). Maybe a dislike of going barefoot, something like that? Linnet's been ice skating so there's not an actual hatred of the counter element in that sense.
I'm probably rambling but hopefully that helps a bit!
~ Carys