Recent research has shown that nuclear winter after even a limited exchange would be worse than previously thought. We don't know how/if our technological society would bounce back from N billion starvation deaths.
Indeed, just 100 small warheads would (maybe) do it. See Mills' Multidecadal global cooling and unprecedented ozone loss following a regional nuclear conflict [0] which models the effects of a limited nuclear conflict between India and Pakistan.
I believe you misunderstand the cause of a nuclear winter.
The cause isn't the nuclear radiation per se. It is the extreme destruction of many large urban centres simultaneously. The problem is that all of those cities burning simultaneously would send up a tremendous amount of ash and smoke that would block the sky for quite a while.
This would cause a reduction in the amount of sunlight that would be available for growing crops and combined with the almost total destruction of global economy could result in the destruction of the entire human race through mass starvation.
[0] http://onlinelibrary.wiley.com/doi/10.1002/2013EF000205/full