According to Wikipedia over 2000 nuclear tests have been performed since the Manhattan Project. If nuclear war would bring about a nuclear winter, why didn't testing do? Were they too much spread out in time to cause any real climate damage?
A nuclear winter would be a result of large amounts of smoke blocking light from the Sun. The smoke would be from the fires started by nuclear bombs on cities, not directly from the bombs.
Most bomb tests have been underground, and the above ground tests were mainly done where there wasn't much to burn, for example in the Nevada desert so they didn't generate any significant amount of smoke.
Burning cities and volcanos affect the weather in much the same way but for slightly different reasons. Volcanos produce sulpher dioxide aerosols while burning cities produce carbon dispersions, but both reduce insolation. In both cases their effect on the weather is only marked if they manage to get a significant amount of fine material past the stratopause. Anything in the mesosphere gets rained out too quickly to cause much change, but once into the stratosphere smoke/dust can persist for several years and reduce the light reaching the ground. Rock vaporised by a nuclear explosion will condense quickly and is unlikely to reach the stratosphere.