I know you can write applications for the Zune, but what about the Zune HD?
Doesn't sound like it -- see here:
Zune HD will indeed be getting applications, but at this time Microsoft is planning to keep the development in-house. In those situations where they do want to work with a third-party developer, it will be a close relationship with the Redmond,WA-based software giant. In other words, you won’t be seeing the wild west frontier mentality that we have seen grow up around the iPhone, iPod Touch, Google Android and the Palm webOS. At this time there will be no independent software development kit (SDK), although Microsoft does not rule that out for down the road a ways.
...and also here.
After much research on Google I have determined that the Zune HD is likely, but not officially confirmed, to have support for XNA. If it does have support for XNA, you will be able to create apps for it, although those apps will likely be games as XNA is primarily a game development framework.
UPDATE: XNA Studios just added Zine HD support. So yes, you can at least make games for Zune HD as well as any other app you can make with XNA.
Answer:
http://coolthingoftheday.blogspot.com/2009/09/xna-game-studio-31-zune-extensions.html
yes. And, while XNA targets gaming, normal apps are usually less complex, so IMHO there's nothing that says you won't be able to deliver normal apps as well as games that target the HD.
Mine's already shipped.
Ever heard of OpenZDK?
"That’s about to change. Through the work of myself as well as Netrix, Nurta, and the rest of the ZuneBoards Development Front, all Zune models, including the Zune HD, have been hacked. The first true hack available for the Zune, this makes it possible to, for the first time, run applications directly on top of the Zune firmware, with full access to everything XNA withheld before. The limitations of XNA are now no limitations at all." (from Zune Boards: http://www.zuneboards.com/?p=vB50442)
The OpenZDK wiki: http://zunedevwiki.org/wiki/
Personal experience: I have used XNA games on the Zune HD along with the Zune 30...works great!