How about some Advent hymns?
You will not believe how beautiful they are. Learning these songs ourselves and singing them together as a family will go a long way to healing the insanity brought on by Feliz Navidad (why is acceptable, in an otherwise aggressively secular atmosphere, to play a song that refers to the religious event, however obliquely, and however obnoxiously delivered, just because it's in Spanish?), Frosty the Snowman (odious creature), and Let It Snow.
It's an insult even to mention these titles in the same post as one on Advent hymns. But maybe we can change our present culture if we, little by little, make more known the treasure trove of lovely hymns for this season.
Better to light a candle than curse the darkness, as can be aptly said of Advent!
So, look here for some words and MIDI files. (Children particularly love On Jordan's Bank.) It's worth getting a traditional hymnal for the family, such as the Adoremus Hymnal-- and why not get the choir version so you can learn the harmonies?
A more recent song by Eleanor Farjeon is a favorite here: People Look East.
This should keep you busy for a while. Even if this year the little ones learn O Come, O Come Emmanuel, a medieval chant that contains Scripture and prophecy, you will have made great strides against the snow/jingle bells/chestnuts incursion.
Catholic Culture is a great resource for doing little or much (full disclosure: this is the home of the Chief's site, Catholic World News) in living the Liturgical Year. Click on the tab of that name and be amazed at all the resources that are already in place for you! This article from Christmas to Candlemas in the Christian Home is a good start!