I am looking to travel during the month of December, during Christmas. I am wanting to travel somewhere that has mountains, and a very "Christmasy" feel.
Austria (Tirol), Germany (Bavaria), Italy (Südtirol), and Switzerland are all good bets.
For example: Stay in a city like Innsbruck for the "Christmasy" feel. Stay in a valley near Innsbruck for the mountains (and skiing, snowshoeing, etc.)
Be aware that winter is the high season and Christmas is the highest of that high. Bring a thick wallet and a stack of credit cards.
@ap_30 you might check out Leavenworth, WA - the town calls itself "the Alps of Washington" and boasts a Bavarian theme. They go big for Christmas, with lights and events throughout the month. Also, you're nestled among the mountains, which means you've got tons of outdoor recreation to keep you busy and active!