"It is important to clarify that we are not contemplating a situation of either abrupt cooling or global warming. Rather, abrupt regional cooling and gradual global warming can unfold simultaneously. Indeed, greenhouse warming is a destabilizing factor that makes abrupt climate change more probable. A 2002 report by the US National Academy of Sciences (NAS) said, “available evidence suggests that abrupt climate changes are not only possible but likely in the future, potentially with large impacts on ecosystems and societies."

I am unconvinced greenhouse warming is a destabilizing factor, but do agree that it seems reasonable that regional affects are probably more important than global changes in temperature [warming or cooling]. I would say that the most significant destabilizing factor in global changes in temperature are regional changes.
Said differently, global warming or cooling are not indications or drivers of global changes in temperature, rather regional changes drive global changes in average global temperature.
For example, I don't think it's likely that you could have a cold Europe and a globally warm planet, but it's possible that a cold North American could have a greater affect on cooling the world than compared to equally cool Europe.
I think the regional affect driving global temperature is already proven to be true. It's quite simple, the location of the Antarctic continent at the South pole is the reason for the last +50 millions of Earth being in a generally cool period- If the south pole were open ocean instead of having a continent, Earth would be considerably warmer. Two vast oceans at both poles would give us the warmest conditions- meaning an small enclosed ocean at either or both poles is a different situation- as would having a large archipelagos at the polar regions.

Now, is it possible for Europe or America to get colder, I think the answer is obviously yes- if glaciers started growing and continue to grow significantly- meaning more snow fall during the winter this would cause these areas to get cooler. Adding 10' to snow packs on average per year over a 100 year period would have a very significant affect upon regional temperature- this has little to do with temperature and everything to do with significant increase in the quantity precipitation during periods when it normally cold.
And obviously if you add more on average it takes less time- 20' per year in 50 years, 50' per year in 20 years. But regional average temperature could remain the same or even warming, and appear to get colder in a much shorter timeframe- because it would "snowball".

The question of course is how did we get out of the deep freezer, not whether there is any chance of us entering the oven. And of course is there any way we could possible avoid heading back into the freezer and whether or not this possible when will this occur?
I do think we will find these answers by understanding the oceans better.