The Ice Cap itself essentially covered the entire boreal forest. Rather obviously, the Great Lakes did not exist at all. what did exist was Lake Agassi which covered lands from the Boreal Forest to the rocky mountain foothills and southward down into Wyoming abutting the Colorado river Basin in particular and surely some part of the Mississippi basin. All this means that for the five million years that the ice age was active, this lake exited by way of the Colorado river. Also recall that the rocky mountains were also hosting the Columbia Ice field. However you tell the story it is obvious that ample water scoured the sedimentary stack we see in the Grand Canyon. and this all changed 12,900 years ago.