It doesn't ring a bell, but it may with another Barry fan here.
The short version is, on a frigid Christmas eve before dinner Dad tells young Dave Barry to go out back and feed the goat; he comes back inside to whisper to Dad that the goat has frozen to death; Dad suddenly remembers something he needs at the store and he and young Dave put the frozen goat in the back of the pick-up and drive off into the blizzard to look for a place to dump it; they stop in front of a church and add it to the Nativity scene on the church's lawn; the freezing weather persists, and a week or two later they go to retrieve the goat, only to find the creche is gone; they ask the church handyman where it is, and he says we store in the church basement in the furnace room until next year.