Sprinkle ordinary ground pepper on the skirt, or base of the tree and on the lower branches, and your cat will sneeze and leave! It’s harmless and won't affect your cat or damage decorations.
There are also sprays, such as bitter aloe, sold in both pet stores and pharmacies. Spray a little on the lower branches and the chances are your cat (and dog) will be discouraged to return. Sticky sheets usually used to deter scratching on furniture will also work when placed around the base of the tree. Kitty will soon get the message that Santa only has gifts for nice cats and not naughty ones! Also, consider putting any special gifts for your cat out at the very last moment, especially if catnip is involved. The feline nose knows.