Yes, they do.
Tip #1- tie all wiring down. Cats can chew on the wires if they hang. Besides the obvious demise seen in Christmas vacation (kitty fireball), there is a lot of lead in these wires.
Tip #2- I have a fake tree because no matter how hard I tried, I couldn't get the cats to stop drinking the water with that tree saver powder mixed in it. I'm sure it's not real good for them. The tree is pre-lit so it's less hastle and mess also. And don't let any breakable ornaments hang low on the tree. Use twist ties or crimp the metal hangers tight on the branches so if they bat at them, they stay on.
Tip #3- If you put the tree in the corner, and stack gifts or other items in the back first, you are less likely to have them hang out behind the tree causing mischief where you can't see them.
Tip #4- Do not let the cats in the house at all durring the holidays, and put what ever you like anywhere you want with out a single worry.
Just kidding.
Tip #5- get the cats thier own little sparkly things to play with to keep them interested with that, rather than your decorations.
Tip #6- have a happy holidays and enjoy it with your precious furry friends!