As mentioned in comment #3 you can use
https://mail.example.com/h/ from an iPhone today. It's rather squeezed, but functional. That's more of an act of desperation, though... proper support should be coming in June.
Re comment #2, it's not just Zimbra that cares about iPhone ActiveSync working with Zimbra. If you look at
Apple - iPhone - Enterprise - Apply you'll see several versions of Exchange, Lotus Domino, Kerio, and Zimbra as things Apple considers worth participating in their beta.
There are some RFEs for allowing creation of contacts & appointments in the /m/ interface, but given that better options are available or soon-to-be-available on pretty much all devices, I wouldn't prioritize it.
ActiveSync is a Zimbra NE-only feature... but if you can afford an iPhone, you can afford NE.