It's speculation on my part, but I would really doubt they were three miles thick, especially where the plains and mountain valleys were ice-free.
Still, the slogan "tis a pleasure to live in Colorado" probably wouldn't have been coined during the last glacial max. :-))
Three miles of ice makes me skeptical too. That would be more ice than the mountains are high from sea level. But I did read that theory somewhere. I’m just glad to be here now speculating about it and I hope it keeps warming.