(Works best in an smaller geographic area, and takes one class activity to prepare, and a combined youth activity for card delivery.)
Announce in Sacrament Meeting or on your bulletin that the youth will be delivering Christmas Cards to members of your ward or branch. Our unit collects the cards in a box in the foyer that is decorated and placed there the first Sunday after Thanksgiving.
For a class activity, have the youth decorate paper sacks to hold Christmas cards for each family in your unit.
Then as a combined YM/YW activity, deliver the Christmas cards and bags while caroling to the families in small groups, or however works best for your area and group.
Visiting and Home Teachers may also want to send cards to families on their routes with your group.