Does Cone of Cold kill you if you drop to 0 hit points?

@JeremyECrawford Does Cone of Cold kill you if you drop to 0 hit points?

— King Wizard (@_Matafer) June 24, 2016

Cone of cold would say if it killed you at 0 hp. It doesn't. It does say it turns you to ice if it kills you. #DnD https://t.co/nrzvjeiKR5

— Jeremy Crawford (@JeremyECrawford) July 21, 2016