Is this the usual way one would refer to iced coffee, or would that be es kopi, like es teh?

That would be "es kopi" , "es teh" , "es cendol", "es kopyor", "es teler".
That would be the way to refer to iced drinks.

To my ears, I like coffee cold means I am still interested in drinking coffee made hot when it becomes cold. I like cold coffee means I like coffee that was made to be drunk cold. That's just the connotation to my ears, though.