"Destroying the planet" doesn't mean nuking every single square-inch of land. Models predict that it is possible to trigger a self-sustaining nuclear winter when soot blocks the sun.

Destroying the planet via nuclear winter is firmly within our grasp, and we have enough nukes to do it several times over.

Nuclear winter theories have been discredited. The science behind them was always fairly shaky--it requires several massive firestorms to trigger and generate stratospheric clouds for the global transport. Yet firestorms don't seem to cause stratospheric plumes, and there is good reason to doubt that modern cities are capable of producing the firestorms in the original model.

Looking at relevant experiences, there is even more reason to doubt the models. The Kuwaiti oil fires--where Iraq basically set an entire oil field on fire, and lasted for a month--failed to produce anything more than an intensely local problem. Even volcanic winters are probably overblown: there is only one well-documented case of severe effects of a volcanic winter (Year Without a Summer), and that required some exceptionally bad timing. While researchers do tend to make a game of linking famines listed in historical records to historical volcanic eruptions, it's not at all clear how correct this linkages are, especially since it shows clear signs of selection bias (no consideration of large volcanic eruptions that may not have produced volcanic winters).

There has been some modeling work that suggests an India-Pakistan exchange, let alone the US throwing down, would alter the climate enough to have far reaching impacts the world over.

"Destroy" doesn't necessarily have to mean "Glass"