Gods, no, the ones we use as mounts are nowhere near that big.

[A pause.]

Though, it's likely we're thinking of entirely different creatures. Wyverns are certainly dragon-like, but they're only just a bit bigger than a large pegasus. It's only the wild ones that prey on people, many of the domesticated ones wouldn't do so. Though that hasn't stopped someone I know from threatening to have hers eat people who anger her.