Check your expectations
Don't set the kids up for disappointment by trying to make the holidays "just like they used to be." They won't be just like they used to be, especially if you've met someone new and are trying to combine "yours and mine." One of the biggest mistakes divorced parents make is trying to recreate a past family tradition with a new partner.
Here's one scenario: Daddy used to dress up like Santa Claus each Christmas Eve, so this year, in order to carry on the tradition, your new partner dresses up like Santa Claus. Although you may be trying to ease your kids' pain by orchestrating something like this, what it really does is put the new partner in direct competition with Daddy. Rather than make things better, it simply reminds the kids that Daddy and Mommy are no longer together. This scenario may actually increase their anxiety rather than ease their concerns.
You can get creative, but remember that you're not in competition with your ex. It's about creating lasting memories and an environment where the kids look forward to spending time at both houses. And, as divorced parents of the same kids, it's your responsibility to cooperate in their best interest.
Make new traditions
If you're now a single parent, look for ways to integrate past family traditions into your new lifestyle. If you've remarried, modify them to suit your new bonus family.
Here's a scenario: If decorating the Christmas tree is a family tradition, and the children are now going back and forth between homes, why not pick out a tree weeks before Christmas Day and decorate it ahead of time?