Well, the radioactive dust and soot is thought to last for several months, plunging the earth into a mini ice age but the radiation contamination would last for centuries.
For instance, even now, whenever a storm big enough passes through japan, radioactive sediment is stirred up from Hiroshima bay. From the bikini island tests, we know that the coconut trees are sucking up selenium and other nasties and concentrating them in the fruit... we found this out after the residents of the islands moved back and started dying off in high numbers from cancer even though the islands had been scrubbed "clean".
So even if we could get food to grow, the plants would just suck up the contamination.
Just from what's shown in T1-4, there's no reason to assume it was a full out nuclear holocaust. Large parts of cities and urban areas are left standing even if they are decimated. But considering how everyone is bundled up, enough of a war to spark a global cool down.