Artificial trees are also dangerous when eaten. The principal things to worry about are toxin release from the artificial material and an intestinal obstruction. It really depends on how much is consumed. Many times, pets don't consume mass quantities of tree material. Please confine your pets away from the tree when you are not home. This will allow you to supervise any tree or plant eating activity. Other plants, such as Mistletoe and Holly are also poisonous.
While we are on the subject of Christmas trees, also consider the tree water. Preservatives, pesticides, fertilizers and other agents, such as aspirin, are commonly used in the tree water to keep the tree fresh. These may have harmful or deadly consequences for cats and dogs who drink the water! A covered tree water dish is the safest.
Christmas lights, on the tree and elsewhere in the home also pose a hazard to curious pets. Chewing on cords and lights will cause electric shocks and burns in the mouth. Check cords regularly for signs of chewing and general wear and tear. If you notice that your pet is reluctant to eat, drooling or showing signs of a painful mouth (i.e. not wanting to play with regular toys) be sure to rule out electrical burns in addition to dental and other diseases.
Holiday ornaments also pose a risk. Ingestion of ornaments can cause gastrointestinal blockage or rupture. Depending on what materials were used to make the ornament, toxicity may result if ingested.