It would seem that there was magic in creating a flying half-bird, half-horse for Harry Potter and the Prisoner of Azkaban and USA Today and MSNBC both have information on the process.
In the USA Today article they discuss how it took two years of computer work to create Buckbeak and that even he had a stand-in.
"The hippogriff was probably one of the most complex creatures we've ever done (in the three Potter films)," Potter producer Mark Radcliffe says.
In the MSNBC article, which includes video, you actually get to see how they created each of his feathers and how they all moved on screen via computer.
"We spent a lot of time down at the zoo," says CG supervisor David Lomax, "going to bird sanctuaries to study their movement and what they looked like, as well as taking many pictures of horses and studying horses in fields."