There are some pretty creative dragon designs in the movies/show. Are any of these inspired by or based on old stories and legends or are they all developed for the movies/show?
According to the author, the inspiration behind the dragons came from a mixture of sources, not only the classic dragons of mythology and the more modern dragons depicted in Tolkien but also other large predators:
Although I really enjoyed books about dragons as a child, such as Tolkein’s [sic] ‘the Hobbit’, I always wondered why they always seemed to look the same, like a big green lizard with wings. Surely dragons would have developed along the same lines as dinosaurs, into all sorts of different species, specially adapted to their environments in different ways?
I have great fun creating all these species. I mix up different real-life creatures to make a new fantastical animal. For instance, in How to Break a Dragon’s Heart’, I had a giant Bee-eating dragon that was a mixture of a Basking shark and a giant ray. It glided through the treetops with its mouth permanently open, to catch bees rather than plankton. And then there are chameleon dragons, and see through dragons, and dragons with horns on the ends of their noses like narwhals…great big Seadragons many, many times larger than a Tyrannasaurus [sic] Rex, and teeny little nanodragons no bigger than your fingernail.
As to the inspiration behind the dragons depicted in the film series, there's a truly excellent blog post here going into great detail about what the makers were aiming to portray and that quotes extensively from a range of sources including the HTTYD art books, making of featurettes and director commentaries:
Deadly Nadder (Stormfly)
Stormfly, actually, interesting, is supposed to be modeled after a bird. You can really see it in the way the dragon hops around lightly on its feet and preens itself. Head of Character Animation Simon Otto described the Deadly Nadder species as a dragon which “moves like a parrot, with a bit of an emu’s walk and the posture of a Tyrannosaurus Rex tossed into our blend of behaviors.”
Zippleback and Monstrous Nightmare (Barf and Belch, Hookfang, Fanghook)
It’s not really specified anywhere I’ve found if these dragons had particular animal species models. The Monstrous Nightmare is a dragon from the original novel series, and the art book for HTTYD 1 says its design is the most “classical dragon”.
I feel like the Zippleback has sort of similar treatment, but I have no sources to give you on that. A multi-headed dragon is just something that is somewhat classic literature-wise and we’ve seen before, so I feel that’s where it came from conceptually. Also, even though the tenth book of HTTYD hadn’t yet been published, the directors consulted author Cressida Cowell throughout the movie-making process. The fact that DreamWorks originally planned for Fishlegs to ride the Zippleback (he has a three-headed dragon in the books) seems like no coincidence to me.
So I think these two dragons have the most “standard dragon” features and less branching out to other real species. But if someone knows more and can correct me, I’d love to hear it!
Information about the Gronckle’s character design doesn’t appear in the art books, but a HTTYD 2 special features clip found here reveals that this dragon is a cross between a bulldog, helicopter, and bumblebee.
Terrible Terror (Sharpshot, Sneaky, Butt, Head, Pain, and Iggy)
The Terrible Terror was the original “Toothless” back when the movies were going to stay truer to Cressida Cowell’s novels. The design also, however, includes “flying squirrels, salamanders, and one particular behavior of a desert gecko that prances to keep its feet cool on the hot sand,” to again quote Simon Otto from the HTTYD 1 art book.
I am guessing that the Hideous Zippleback was based on a snake, as well as a couple of other things, since snakes have scales, some are green, some are venomous (Fishlegs, in the first movie, said that this dragon injects its prey with venom!), and, really, can anyone honestly say that their necks aren't snakelike?