I'm not sure what's meant by "skullies," but maybe what's being mentioned is:
http://en.wikipedia.org/wiki/Flat_cap
Ok; now I get it. As a proper Bostonian-in-exile, I know them as "scally caps". I have a nice navy blue one that was make in Killarney. I don't have any that would be light weigh enough to wear in the summer, so I wear baseball caps if I wear anything at all.