that's not an accurate summary. https://en.wikipedia.org/wiki/Nuclear_winter#1980s - during the early development of the theory, they believed that the Martian models were directly applicable and a good analogue for dust movement.

Modern analysis concludes Nuclear Winter would still likely be a very real thing - https://en.wikipedia.org/wiki/Nuclear_winter#Recent_modeling

Most modern debate is only around how bad it would be, not whether it is real.