According to the Wiki Dragons do NOT have the BEAST Attribute.
They all have DETECTOR and GIANT, the Rumour Dragons, Red Dragons and Elder Dragon have FIRE ELEMENTAL, the Zombie Dragon has TOXIC AURA (but not UNDEAD) whereas the Nightmare Dragon has OUTSIDER and UNDEAD (but not GIANT).
Of course I can't say for certain if the Wiki is correct. I'd say Zombie Dragon should be UNDEAD, and White Dragons should have ICE ELEMENTAL.
Perhaps Green Dragons could be more "natural" (vs the Ice & Fire types of Dragon) and have the BEAST attribute added?