You don't lose your warranty by installing an unsupported OS. The computer manufacturer simply won't provide any free technical support you may otherwise be entitled to if you have problems or questions when using an unsupported OS. You may also have problems obtaining authorization for repair/service without first restoring the supported OS, unless the system just won't boot or power-on.
Your school probably has some volume/open licensing agreement that would govern downgrade rights. The downgrade rights in such an arrangement would not be extended to you, only to the institution, who may then be able to authorize it for their users.
BTW, I frankly don't believe this story about getting $200 refund on pre-installed Vista Home Premium. If its true, then it was a screw-up on HP's part. At the most, the preinstalled OS only adds $30 to the purchase price of a computer system shipped by Royalty OEMs such as HP, Dell, Gateway, and the like.
As with large volume licensing accounts that have thousands and thousands of users, large OEM computer manufacturers who ship millions of computers get huge volume-based discounts on the per-license cost of Windows or other applications that they ship.
I think someone at HP mistakenly typed "$200" instead of "$20". lol!
