A 'cobalt' bomb isn't some mysterious doomsday weapon. It's a any thermonuclear weapon with ordinary cobalt metal (59Co) as part of the tamper or other component. The cobalt absorbs some of the bomb's neutrons to become cobalt-60. The half-life of cobalt-60 (5.27 years) means that initially the effects of the other fission products dominate. However, it stays around a long time and renders affected areas dangerous to habitation, much like the Chernobyl exclusion zone.
Spread enough cobalt-60 across, say, the American midwest, Canada, and the heartlands, via a few high-altitude airbursts, and the food system is likely to collapse because the arable land is too contaminated.