Just spotted this on GWHoops.com: poster NJColonial put up a GW logo sticker on his Madsion Hall room in the 80s, and it's still there. Pretty cool of the dorm staff to let him see if it's there. (It was hidden behind some furniture.)
He says it was from the football era, which ended in 1966, and I agree just based on the style: a jaunty, scowling colonial (George?) in a frilly shirt. It reminds me of those 1960s live action historical TV shows. Pretty awesome.
(And kudos to poster Dootie Bubble for the Photoshop to make it more readable.)