The Freeview HD spec mandates an ethernet port, and it includes the same MHEG-IC ("Interaction Channel") extensions as Freesat. So, in theory, iPlayer or 4OD can be delivered over Freeview HD in the same way as it is over Freesat.
Right back at the launch, however, Freeview said they weren't playing that up, and it would be largely up to manufacturers to decide what to do with the functionality. I think part of that was because they simply wanted to concentrate on pushing the HD message, without muddying the waters with talk of IPTV too - and perhaps the delays to rolling out the Freesat equivalent made them less willing to shout about it at the time.
Nevertheless, the revised FreeviewHD testing scheme certainly includes support for the MHEG-IC functions, and it's fairly widely expected that iPlayer will be rolled out this year.
When that happens, I suspect it will follow a pattern similar to Freesat, where the BBC tests their service, and when they're happy, other broadcasters launch theirs, confident that the platform itself has been debugged.
In the meantime, box makers who want to differentiate can provide iPlayer access using other mechanisms, as found on the iCan box, for instance, and shortly to be available on the Humax ones.