Barbara, I think it's Furry Day Carol, but I don't know the lyrics. And, I don't know whether you specifically meant Anglo Saxon when you referred to "old English" poetry. I think that any Old English/Anglo Saxon (i.e. Germanic-related) poetry is more likely to have Christian than pagan themes, but there are some throwbacks to pre-Christian beliefs hidden in there. Beowulf springs to mind, i.e. the "monster from the deep lagoon" type of stories, but I think that pre-Anglo-Saxon or Celtic themes would have more interesting stuff in them for researching pagan beliefs.
Are there any songs about The Green Man? I seem to remember hearing one, maybe in relation to a very strange television drama series of the same name at least a decade ago.
Also, the Mabinogion is one written source of Welsh folk stories. There might be something worth looking at in there. I don't know exactly when the Mabinogion was written down, so there may be later social and cultural influences in it as well.