“For her sake, Ned had built a small sept where she might sing to the seven faces of god, but the blood of the First Men still flowed in the veins of the Starks, and his own gods were the old ones, the nameless, faceless gods of the greenwood they shared with the vanished children of the forest.” (AGOT)
“The gods the children worshipped were the nameless ones that would one day become the gods of the First Men—the innumerable gods of the streams and forests and stones. It was the children who carved the weirwoods with faces, perhaps to give eyes to their gods so that they might watch their worshippers at their devotions.” (WOIAF)
Revelations about the weirwood network of long-dead greenseers aside, what followers of the Old Gods actually believe is a straightforward case of animism.