Will upgrading Mac Mini hard drive void AppleCare Warranty?
Apple's warranty (AppleCare) is specific about what components are user replaceable/serviceable. The hard drive on an older MacBook for instance is user replaceable, AppleCare used to have the option to send you a replacement hard drive along with a disposable ESD wriststrap for you to install it yourself.

The difference though is the hard drive in the MacBook was almost as easy to access as the RAM in the Mac mini. The Mac mini's hard drive is a different story. In order to access it you have to expose the logic board which increases the chance of damage from ESD if proper precautions aren't taken. Because of this the only user replaceable part in the new minis is the RAM, since the logic board is still pretty well protected when only removing the RAM.

The Magnusson Moss act essentially says they can't deny warranty unless they can prove damage. It wouldn't be hard for Apple to say "The upgrade situation you described to us implies that there was a high risk for ESD damage, which has likely caused such and such issue".

The flip side though is that if an Apple Authorized Service Provider (AASP) installs a third party hard drive your AppleCare will remain intact because the AASP has proved to Apple that its technicians follow all safety rules and procedures when working on Macs, essentially the same reason Apple allows them to perform warranty work. Apple would then not be involved in the hard drive's warranty (though most HDDs have 3-5 year warranties of their own) but the remaining components would still be recognized as "in warranty" by Apple. The most you would need to do is provide a receipt for the service you had done at an AASP.

source: I was "that guy" at the Genius Bar for several years who had to turn people away from warranty coverage for unauthorized upgrades &amp; repairs.  As soon as your Mac goes out of warranty I definitely encourage a DIY attitude, however I would try to heed the above advice while it's under AppleCare.