Here's a multi-movement work called 'Noels en Trio' by Michel-Richard de Lalande (1657-1726) which would work for two violins and cello: score / violin 1 / violin 2 / cello
Here's a link to where you can download an arrangement of Corelli's Christmas Concerto op.6 no.8 for string quartet (score and parts available). The files are zipped... Corelli: op.6 no.8
The First Noel arranged for piano trio: piano / violin / cello
The site music-scores.com has some Christams carols arranged for string quartet available for free. You are allowed to download 3 files per day if not a paying subscriber to their site.
Here's some Christmas Carols from various sources that could be played in a string quartet at Christmas-time gigs if your violist can read bass clef...
O Come, All Ye Faithful
Ding Dong Merrily on High
Go Tell It on the Mountain
Away in a Manger / different version of Away in a Manger
Good King Wenceslas
Hark! The Herald Angels Sing
Joy to the World
O Come, Little Children
O Little Town of Bethlehem
O Christmas Tree
Coventry Carol - first page has trio version, pages 2 and 3 have quartet versions.
I Saw Three Ships Come Sailing In
The First Nowell
The Holly and the Ivy
We Three Kings of Orient Are