Depends on the weapons (nukes aren't my strong point, though I seem to think Skashion is pretty up on his military stuff), though I can't see the radiation lasting for longer than 100 years to a fatal limit.
The idea is that they dust blown up into the atmosphere would block out the Sun for a little while, but when it started settling after a few years, the light that did get through would be enough to create the greenhouse effect, which would melt the CO2 ice caps, thickening the atmosphere a bit, resulting in further greenhouse effects, which would in turn melt the frozen water, making the atmosphere a bit more hospitable. It would need to be managed correctly, and obviously it's only theoretical, but there aren't too many reasons why it wouldn't work.
The idea is that they dust blown up into the atmosphere would block out the Sun for a little while, but when it started settling after a few years, the light that did get through would be enough to create the greenhouse effect, which would melt the CO2 ice caps, thickening the atmosphere a bit, resulting in further greenhouse effects, which would in turn melt the frozen water, making the atmosphere a bit more hospitable. It would need to be managed correctly, and obviously it's only theoretical, but there aren't too many reasons why it wouldn't work.