According to the Wikipedia entry in anonymous's Google search link, the hippogriff was first mentioned by the ancient Roman poet Virgil, in his Ecologues. (Book VIII) He doesn't give the creature a name, just uses the example of gryphons mating with horses to comment on a human relationship that seems equally unlikely.
The Roman emperor Augustus built a temple to Apollo decorated with a hippogriff and dolphins. So we know that 1st-century Romans would understand a reference to a half-horse, half-gryphon. That doesn't necessarily mean that the hippogriff was a symbol of Apollo, however. The temple was built after the battle of Actium, so the dolphins are a reference to the sea battle, and the hippogriff may be a reference to Egypt.
Orlando Furioso may well be the first to give it a name, and a good name too. In any case hippogriffs aren't mythological per se - they feature in no myths. They're imaginary animals, and can carry symbolic freight, such as this idea that their parents are mortal enemies and so they're a symbol of love.
The oldest source I could find for the idea that gryphons and horses are enemies is Isidore of Seville, from the 7th century CE.
(Apparently in medieval times the unlikeliness of horses and gryphons mating became a proverb.)