While the AMD "Trinity" APUs are out there now for notebooks, Hondo is AMD's upcoming Fusion APUs targeting tablets that carry a sub-4.5 Watt envelope while packing one or two processing cores and integrated Radeon graphics. Like Intel's Clover Trail, Hondo should be hitting around the time Windows 8 arrives and various hardware vendors are already working on new Hondo-powered tablets, but only using the new Microsoft OS.
AMD's Steve Belt confirmed to The Inquirer that initially this ultra low-power APU will be a Windows-only product. Linux/Android support isn't being ruled out entirely, but they are giving Microsoft exclusive rights at launch. Aside from The INQ, I've heard this Hondo-is-for-Windows information elsewhere. If querying the Linux kernel commit history you will see nothing that references Hondo. (Update: For clarification, the INQ source does indicate, "However unlike Intel, AMD said there is nothing stopping people from running Linux on its Hondo processor.")
AMD's Hondo APUs may end up working fine under Linux since they are x86_64-based after all and using Radeon graphics. With the Catalyst driver consisting of largely shared code between platforms, there will hopefully be support within the Linux driver and for the graphics driver on the open-source side it will hopefully come down to sprinkling in the new PCI IDs. But the Linux support may come up short when it comes to the power management/performance and other optimizations. We'll have to wait and see in the coming months.
Like Clover Trail, Hondo will hopefully be a one-off stint with Microsoft. In 2013 we will see new 28nm Fusion APUs out of AMD that should be more interesting anyways, but what will be interesting to see is how the battery life and performance-per-Watt compares between Windows 8 and (non-Android) Linux on next-generation tablets.
The other positive takeaway is that with these announcements of Clover Trail and Hondo support not coming to Linux, it's generating mainstream interest on other sites, compared to it being an announcement in the past when a product is supported on Linux.