Skip the cold, and stick with heat. And heat it until cherry red. Then whack it with a dead blow before attempting to twist it out. If upon twisting, it's still stuck, tweak it clockwise, then counter-clockwise. The heat will help it expand, the whack should un-seize it, the twist should turn it loose.
Even welding it, should produce enough heat to free it right up. The welded on nut should make it quite simple to turn out. Lots of folks have dealt with this even being experienced and careful.