Christmas time is supposed to be a time to be festive and happy, but it may be difficult to be in a festive mood when you're dealing with someone you can't stand. Indeed, co-parenting with an arrogant and clueless person is no picnic, and you may want to do everything in your power to keep him or her out of your life; but if you have children together, it is critical that you put your differences aside for them.
The holiday season can be impressionable for kids. After all, you probably remember some of the great Christmases of your youth. Now think about how those memories could have been (or were probably) ruined by knock-down, drag out fights with your ex.
If you think that you are incapable of making a truce for Christmas, consider how the Germans and British found a way to do so during World War I. Essentially, the two armies climbed out of their trenches, laid down their weapons and took time shake hands and bury their respective dead. As the story evolved over time, it has been reported that the two sides even played a soccer game. (The game was even depicted in a Christmas commercial for a British retailer).
With that said, it shouldn't be impossible to strike a truce with your former significant other during Christmas, even if it means giving up time with the kids. Ideally, the kids would want to see you together, so keep that in mind as you consider laying down your weapons.