nuclear war is a myth with no basis in actual science.
Even Carl Sagan who heavily promoted the concept admitted that he did not have the evidence to support it.
The meteor that created Meteor Crater hit with an estimated impact of around 800 megatons IIRC (equivalent to about 2,400 average nuclear weapons) and it didn't cause substantial climate effects.
on Carl Sagan, TRAPS group used today primitive computer simulation of Climate process in 1980s
While Michael Mills used state of art climate simulation in 2007.
Meteor Crater was 15 Megatons of TNT in desert of Arizona
Let take other extreme: Chicxulub, that was Asteroid of 15 km with of 100 teratons of TNT, which exterminate the dinosaur.
85% of mass, the Chicxulub ejected was distributed world wide!
while Meteor Crater remain a local occurrence, like Tunguska with 5 megatons of TNT.
but look on another major impact on climate: Vulcan's
in 1883 the Krakatoa exploded with 200 Megatons TNT.
it's ejected 18–21 cubic km sulfur aerosols and volcanic ash into stratosphere
result the year without Summer in 1884, global temperatures fell by as much as 1.2 °C
Lake Toba a supervolcano in Indonesia
it exploded around 70000 years ago, with 28 gigatons TNT.
ejected estimated 2800 cubic km of sulfur aerosols and volcanic ash into stratosphere.
Toba led to a volcanic winter with a worldwide decrease in temperature between 3 to 5 °C
according anthropologist Stanley Ambrose, it reduce the Homo sapiens population to 10000 survivors.
while cilmat experts making Toba responsible for begin of the Last glacial period.
so that proof the concept of Comet and volcanic winter
it's only needed large mass of ash brought into stratosphere.
But Nuclear Winter has component, missing in volcanic winter: fume and soot aerosols
in nuclear attack cities will be targets, all plastic, paint, oils will burn to fume and soot.
ww2 Hiroshima and Nagasaki had far lest of plastic, as today!
The question is: are enough mass of fume and soot capable of producing a Nuclear Winter ?
according Michael Mills study, Yes