I did this a couple of years ago for the 2017 Christmas season, analysing the choice of songs in 6 Christmas services. Because Cathy was recuperating from serious surgery in December 2018 we didn't actually make it to any carol services at all. But in 2019 I made it to three services, a Methodist evening carol service, an Anglican midnight communion service on Christmas Eve, and the Christmas day service at a non-denominational charismatic church.
The longest set-list was at the Methodist carol service, although they had fewer pieces by the choir this year. The songs featured were:
Once in Royal David's City (solo / congregation)
O Little Town of Bethlehem
Cradled in a Manger, Meanly
Away in a Manger
Born a Stranger (choir)
Come and Join the Celebration
In the Bleak Midwinter (choir)
Jesus is the Heart of Christmas
Hark! The Herald Angels Sing
O Come All Ye Faithful (all 5 verses!)
I quite enjoyed this service because it had a few unusual songs and also we were spared from singing the glurge-dirge that is In the Bleak Midwinter. Born a Stranger was a lovely song while Jesus is the Heart of Christmas encouraged us all to think about Jesus while decorating the house and mentioned tinsel and stockings and stuff.
The sermonette also referenced the Protoevangelium of James. a second century apocryphal book that included a story about Joseph's reaction when he found out Mary was pregnant. As a church history buff with an interest in alternative early Christian writings, I found that quite interesting.
There were four carols in the Church of England midnight communion service:
Once in Royal David's City
Good Christians All, Rejoice (this has been updated from Good Christian Men, Rejoice to be a bit more gender inclusive)
O Little Town of Bethlehem
O Come All Ye Faithful
Looking back to two years ago, this is the exact same setlist as the midnight communion I went to in 2017 in the same church, so it seems they have found a selection they like and are sticking with it. I'm not complaining, these are all great carols.
There were only two "carols" in the Christmas Day service, along with two other songs, which I've bracketed. The songlist was:
The First Noel
(Praise the Father)
(O Come Let Us Adore Him - which is the chorus of O Come All Ye Faithful, but with additional lyrics set to the tune of the chorus)
Joy to the World (with updated, unnecessary lyrics)
The data-set now includes 9 services, and the most popular carol is still O Come All Ye Faithful.
In order, the most popular carols are:
1) O Come All Ye Faithful (8)
=2) Once in Royal David's City (5)
=2) Hark! The Herald Angels Sing (5)
4) O Little Town of Bethlehem (4)
=5) Silent Night (3)
=5) Away in a Manger(3)
I hope to continue this in future years, but I think I will have to try and attend a few different services in some other churches to get a more representative sample.