I have experimented with the idea of a trainable mount that flies between nation states in a manner of hours. As a rite of passage an adult elf will have the opportunity to try and join with one of these flying animals in a mutual respectful partnership, never by slavery or torture. Not all succeed however.\\ 
But what manner of animal are these? Winged of course. Do they prefer flying all the time over walking or running? Do they have four legs and wings or wings and two legs? 
Dinotopia used pterodactyls. The alien movie I recently saw (Avatar) used bird like creatures. Many other stories have used a winged horse and I'm not really taken with that idea.
I can't explain how a winged horse is anatomically possible. You've got the front two legs, the shoulder, and the neck - how can you have a wing in all of that muscle with sufficient strength to lift I have a horse?\\  I think it will definitely be bird like, 13 to 16 feet in length from beak to tail, leather skin with a minimal feathering on the body, more on the wings, a tail which can expand for added control, 10 foot wingspan? Elven homes often include spaces for their feathered mounts to rest.