If I recall correctly, the comet was around 13,000 years ago, the younger Dryas around 11,000 ya. Actually, the comet may have caused a surge of fresh water thus changing the North Atlantic Deep Water circulation and bringing on the cold. Actually concentrated salt when ice freezes in the north is what keeps it going. In fact, a big danger if the Arctic ice melts in the summer is that fresh water will be increased in the North Atlantic, slowing NADW and causing severe winters in Britain and Europe.
Lots of cold, regrowth of glaciers, etc in Europe.
The last big glaciation ended with the Bolling Interstadial, which is a period of warm weather starting about 14000 years ago, and ending about 12,800 years ago.
My preference is to use the major sea-level rises as the touchstone for estimating aggregate global climate however.
If you think of the Bolling Interstadial as being the beginning of the current Interglacial, and with interglacials being typically about 10,000 years long, we are already 4000 years into the next glacial period BUT where's the ice?
If you think of the Bolling Interstadial as a brief interruption of the last period of glaciation, and not as the beginning of the current warm period, then we are about 700 years away from the beginning of the next major glaciation.
If the comet interrupted the current warm period, we are overdue. if the comet simply returned things to normal by interrupting an anamolous warm spell, we have time to waste.
A third view is it doesn't matter because we have gained control of the heating and cooling of the Earth by generating our own clouds, carbon dioxide load and we have nukes if need be.
Given the choice between returning to the world climate of 12 million years ago or letting a couple of miles of ice grind over the United States and Europe, I'll take the warmth any time.
The CoCC authors also refer to a couple of earlier waves of high-velocity debris from the same source.