The glaciers in Ohio were stopped by warmth, not lack of precipitation. The interior of Alaska was just the same during the Ice Age as now. Vegetation, loess, animals, everything. Well, there aren't mammoths or sabertooth tigers anymore, but they would be happy here if they had survived. Summer was possibly shorter then.
Right. That is different from Ohio. Southern Ohio was a TEMPERATURE cut-off, not a precipitation cut-off - and the Carolinas are much further south. Permafrost in the Carolinas is a bit out there.