Is there a Latin origin for 'Twelve Days of Christmas' e.g. first line 'Et parturit in aperto'

I saw a reference to this many years ago and believe that the suggested meaning for the first line was 'And gave birth in the open' with lines 4&3 rendered as 'de collibus, descendens' which translated as 'coming down from the hills'. I do not recall any other lines being given in the source I first saw. It seems to me that the Latin words are too similar to the subsequent English version to be a coincidence and it certainly seems more fascinating that perhaps the original may have been a Latin carol rather than,as I have subsequently been told, some secret aide-memoire to Catholic doctrine during periods of persecution.