Some of these have been covered by multiple artists, and I don't necessarily know who the original artist might be. I'm listing the ones I prefer or I have on a playlist somewhere:

Merry Christmas Everyone, Nathan Evans
Far Away, The National Parks
Heaven Everywhere, Francesca Battistelli
Old City Bar, Tran-Siberian Orchestra
Koppangen, Sissel
Mary, Did You Know? Pentatonix
Mary's Lullaby, Debra Coon West
Christmas Eve, Kelly Clarkson
Christmas Eve, Rachel Holder

There are also several I like from Trisha Yearwood's The Sweetest Gift album, but there's not one towering favorite.