Out of all the events there is to do in L.A. in the wintertime, I recommend making a stop to Disneyland which has "Main Street USA" is all decked out in the Holidays and they have carolers who perform for your Christmas needs.
The beach is still nice to walk on, you may not to go into the water because it is around 50 to 60 degrees, instead of the comfortable 80 to 90 degrees it is in the summer. It is funny that I have a problem with the colder water of the ocean when the temperature in my hometown throughout the month of December is right around freezing.
Well, if you want to a quick break from your arctic wonderland and you live on the west coast, give California a try.