First off: Day9 has a micro tutorial in... some recent daily about dealing with early Hellbats in ZvT. Fantastically done, I think you'd appreciate it. As for Widow Mines, defensive use or offensive? Because with the defensive use, they're not that much of a threat. If he's drone harassing/pulling your troops into them, then I'm not ENTIRELY sure how to take care of it. Unlike SC1, you can't pull mines.
Maybe you could try mixing in Locusts, commence an attack, pull back with your non-Locst units, let them absorb the mine shots, and then run in to kill him. Could PERHAPS try Swarm Host/Infestor/Zergling. Of course Zerglings are gonna get raped by Hellbats, though... Does Infestor/Roach work well against mech?
Fuck zerg. No units designed to take damage from mech. xD Apart from Locust...