The Oxford Book of Carols version is the Christianised set, the English translation of the welsh above is the more secular version. Basically you are singing about the new year coming and how you hope that you don't regret the one just gone, and if you greet the new one singing, you should have a happy new year - start as you mean to go on sort of thing..... Vs 3 says not to ponder on future sadness or anxious care, but to fill the mead cup and decorate the house. It doesn't mention any deity, it is a damn fine tune and everyone can sing fal la la no matter how drunk they are!!To the best of my knowledge, this mead drinking, year welcoming version is the elder of the two, Deck the halls being definately USA in origins. I'm happy to be corrected if that be the case.
LTS