It seems somewhat unlikely that it would ever get that bad. From what I remember, if the gulf stream stopped, then there'd be a 10 degree drop in temperature. We could survive that.
Well the human race would survive, but none of us would be living above the parallel of say, New York City, though more probably Philadelphia. It's hard to live on top of a mile of ice. A one degree average rise in temperature means that some places stay the same, and some places get warmer, and some may even be colder. A one degree (F) rise in temperature over the last century included a more than four degree rise in the Arctic. If that were a linear trend (I doubt it, but), that would mean a ten degree drop in average global temperature would mean a 40 degree drop in the Arctic. That means ice, and lots of it.
If there is lots of ice, the water has to come from somewhere, and we would have a lot less available in the rest of the world.
Even if the ice were minimal a ten degree drop in temperature would mean that we would not be able to grow crops in Canada, the Northern United States, and northern Europe and Asia (including all of Russia). That would mean that the world's population would be dependent on the areas close to or in the tropics. In case you haven't noticed, there really isn't much land there, it's mostly water.