"An Angel Returned" by the Trans-Siberian Orchestra
TSO isn't for all tastes, and (at least in my opinion) none of their subsequent albums have been nearly as good as their first outing, Christmas Eve and Other Stories. However, this song always makes me happy and reminds me to embrace the goodwill, the cheer, and (yes) the inherent cheesiness of this time of year.
"Christmas Bells are Ringing" by Nat King Cole
Although most people default to Nat King Cole's "The Christmas Song," I prefer the cheerfulness and liveliness of this song.
"Merry Christmas Darling" by The Carpenters
This isn't a happy song, but if you are looking for a somewhat melancholy (but not too melancholy) Christmas song, this is the perfect bet.