Andy Turner has a good page of trad songs, with background information
https://afolksongaweek.wordpress.com/2015/12/23/at-christmas-play-and-make-good-cheer/

If you can get Spotify here are a couple of playlists to listen to while you research, might give you some ideas even if some of the delivery is a bit difficult to listen to.
Favourites
https://open.spotify.com/user/headey/playlist/20YSGoSK7bKukDktuGHuyP?si=KUW8hHD0QE61GC3OKrdG0Q

& a bigger playlist
https://open.spotify.com/user/headey/playlist/5vDv2IjNbw3vRy9SP1jroQ?si=aNZfbBajSxigvFs4wCLQIA