The last ice age had a significant impact on human migration, particularly by creating land bridges where ocean had once been. For example, the lowering of sea levels due to the accumulation of ice allowed for the formation of land bridges like the Bering Land Bridge, which connected Asia and North America. This facilitated the migration of people and animals between continents.
While the other options you mentioned—creating new shelters, forming larger communities, and living closer together—might also have been consequences of the environmental challenges posed by the ice age, the most direct and fundamental way it affected human migration was through the creation of land bridges that opened up new pathways for movement.