No doubt about this. Success of many HGs haplogroups depended on "hitchhiking a ride" with farming societies. However the question at hand is about one time frame. Were where I2 in general, or in specific clades, during LGM.
I never voted in this pole though. I think there were few refuge places, which helped bottlenecking, selection and founder affected lucky surviving subclades.
If the question only concerns I2, then the answer is in all LGM refugia. Even north of the Black Sea considering that I2a2a-L699 was found in Yamna, and in the North Caucasus, considering the presence of I2c2 in that region today (but not in Europe proper).
BTW, haplogroup I2's TMRCA is about 21,500 years, which fits right within the LGM (c. 26,500 to 20,000 ybp). Both I2a and I2c were formed around 21,500 years ago too, and top subclades of I2a like I2a1a-CTS595, I2a1b-M423 and I2a2-M436 all existed before the end of the LGM. The post-LGM re-expansion coincides with the appearance of deeper I2a subclades like I2a2a1-M26, I2a1b1-L161.1, I2a2a-M223, I2a2b-L38, etc. Therefore it would be more useful to try to determine from where each of these subclades re-expanded. But it is not that easy as even those top clades were probably very scattered all over the continent. How else to explain that I2a2a-M223 showed up in Early Neolithic Spain and in Yamna? There must have been M223 tribes at least in the Franco-Cantabrian refugium and the Black Sea refugium.
In summary:
- I2a1a-CTS595 would have been present at least in the Franco-Cantabrian refugium
- I2a1b-M423 would have been present in the Franco-Cantabrian refugium, and perhaps also in the Balkans or Black Sea refugia.
- I2a2-M436 and I2a2a-M223 would have been present at least in the Franco-Cantabrian refugium and the Black Sea refugium.
- I2c would have been present at least in the Anatolian and North Caucasus refugia, as well as another on in Europe, possibly Italy.
Not sure where I1 was, but I'd say in the Balkans refugium based on the fact that it was in Hungary when Neolithic farmers arrived. However hunter-gatherers were very mobile, and 12,000 years elapsed from the end of the LGM to the arrival of Neolithic farmers, so it may not mean anything.