Countries possessing nuclear weapons run drills that may train military responsible for firing the weapons to do so for does not matter which reasons. Soldiers unwilling or unable will be relieved from these duties.
If already really nothing else, some may just expect the afterlife, religion unfortunately is sometimes fused with the war machine. Or, more likely, that human as biological species may survive (maybe some tribes in the jungle or the far north that do not use much of the civilization). Or that all humanity is not worth existing.
Due that it is risky to assume that the enemy will not strike back.