Hello- I have found several Welsh"carols"
The best known of course is Nos Galan or Deck the Hall which is actually a New Year's celebration song, originally a harp tune

Others from the standard hymnals
Watchman Tell us of the Night (Aberystwyth)
Come Thou Long Expected Jesus ((Hyfrydol- Rowland Huw Pritchard)
Poverty (All poor men and humble)K.E Roberts / Dr Caradog Roberts
Welsh Carol (Awake were they only)K.E Roberts / Dr Caradog Roberts

hope this helps
julia