Possibly, M.C. While walnuts are not considered to be toxic, all nuts contain fats that can cause gastrointestinal upset, such as vomiting and diarrhea. Foods with high fat contents can also potentially produce an inflammatory condition of the pancreas known as pancreatitis.
Additionally, walnut hulls that are moldy can contain penitrem A or other mold toxins that can produce neurologic effects. Thus, dogs ingesting old walnuts off the ground have the potential to develop tremors and seizures—even possibly even a foreign body obstruction of the gastrointestinal tract, if whole walnuts are swallowed. Because of this, we would advise not allowing your Shih Tzu to chew on or consume these walnuts during your walk.