Nuclear weapons spread vast quantities of highly toxic, highly radioactive dust in all directions, clean into the stratosphere.

Any significant use of these weapons would render the entire planet uninhabitable, and cause total catastrophic breakdown of every ecosystem. Even if you survived the direct attack, there would be no clean air, no clean water - and in a very short time, no plants or animals. The forests and oceans would die, there'd be nothing left to cycle CO2 back to oxygen, the ocean currents would be disrupted, rainfall patterns would be destroyed (even if they weren't coating everything in more radioactive dust), it would be impossible to grow food - the planet would simply stop sustaining life. And that's not even counting nuclear winter, an ice age brought on by the sheer quantity of stratospheric dust blocking out the sunlight (not dissimilar to the meteor wiping out the dinosaurs)

It's hard to cast yourself as a winner if you're shitting your intestines out from radiation poisoning, with no hope whatsoever of anyone at all getting through this.