You could have the climate do the opposite to what we expect and melt the ice caps to flood the world. Our understanding of the climate under extreme stress is pretty poor, so there's nothing to say that we wouldn't kick into a massive heatwave instead of nuclear winter.

As for the larger bomb, essentially anything exploding on the surface is going to do little damage to the earth's surface as the force is instead carried out and up into the air. What you would need to do is explode the device inside the earth's surface where the force of the blast is all transmitted into the crust. So a very large bomb set off inside a major fault line. If it was big enough then the power of fiction could let you have it set off a major earthquake. If you set off lots of them all along a fault line then you'd start to move towards a proper Bond villain white cat stroking moment of horror.