No it's not
Small nuclear war = maybe 10 nuclear warheads explode. Life on most of earth continues more or less as "normal"
Large nuclear war = thousands of warheads, humanity is wiped out
Small nuclear war = maybe 10 nuclear warheads explode. Life on most of earth continues more or less as "normal"
Large nuclear war = thousands of warheads, humanity is wiped out
Civilization OTOH is quite fragile. Hundreds of warheads is likely enough to wipe that out.
How do you adapt to having no food? It's entirely possible that most plant life on earth would cease to exist, with the corresponding collapse across the food chain killing most species of animals across the world.
Any humans left alive would need to eat whatever plant and animal life survived and was available on land in areas that radiation wasn't lethal.. which might be nowhere.
Killing most humans is a lot easier than killing all humans.