Confirmation that the heads' portraits DO roam free at Hogwarts
I don't remember the post, but a while ago there was an argument that depended on whether the head's portraits were as free to roam the halls of Hogwarts as they were to visit their portraits in other locales (Dilys to St. Mungo's, Everard to the Ministry, Phineas to 12 Grimmauld).
Rereading PoA, here's the canon verification; in "The Firebolt' (p. 230 in my edition), Sir Cadogan is found "guarding" the Gryffindor entrance at Christmas entertaining "a couple of monks, several previous headmasters of Hogwarts, and his fat pony."
So yes, the heads' portraits ARE free to leave the office and visit other pictures in the Castle.
Rereading PoA, here's the canon verification; in "The Firebolt' (p. 230 in my edition), Sir Cadogan is found "guarding" the Gryffindor entrance at Christmas entertaining "a couple of monks, several previous headmasters of Hogwarts, and his fat pony."
So yes, the heads' portraits ARE free to leave the office and visit other pictures in the Castle.