Unfortunately, those don't exist in TES lore and that's been the case since way back in at least Redguard. All dragons are two-legged beasts and 4 legged beasts in the TES setting would have to be a different species altogether (I am aware in most contemporary fantasy this isn't the case and two legged dragons are wyverns, but TES is TES and can call whatever it likes a Dragon).
I haven't seen the serpentine dragons up close yet, so I'll reserve judgement.
I don't see anyone pulling hairs if they make the final boss a quadroped. Even so, it can be a different species if it wants, but considering every type of dragon has a different appearances, it'd probably be considered by Bethesda and fans just a different breed, as opposed to a different race. At least, I consider the various types to be different breeds of the same species, but by your logic they'd all be different species because every breed has a different appearance, whether big or small (especially Serpentine and Revered.)