"Happy holidays" is not a part of a "war on Christmas". There are a lot of people in this world that do not celebrate Christmas and instead participate in another holiday tradition. So I believe saying Happy Holidays is a way to broaden the spectrum of whatever you choose to celebrate.
People who believe that there is a war on Christmas need to find something more worthwhile to complain about. Granted, some people to get a little carried away when trying to be politically correct, but in general it is safer to say happy holidays when in non-Christian settings. This doesn't mean that you are anti-Christmas, however.
It is generally more polite to say "happy holidays" than "merry christmas" especially in public locations. The obvious exception to this would be Catholic schools and churches though the former does become contentious from time to time. To all the Christmas lovers out there: Please understand that Christmas is not the most important holiday of the season. When a fellow human being wishes you "a happy holiday," he are(most likely[i am OCD about absolutes]) not being rude. He either does not hold your same beliefs or is respecting such peoples. Have the courtesy to return his greeting in kind. "Happy Holidays!"