Couver is not the one I've had to worry about with the tree... It's always been my cats that try to climb it. It was cute when they were kittens, but not so much anymore now that they are 15 lb cats. This will be Khloe's first Christmas with us, but I don't imagine it being a huge issue, she is usually pretty good.
I guess it all depends on the dog. If they are known for chewing everything, I would be worried