And in the case of hypothyroidism, the thyroid isnt active enough, which can cause a dog to vomit after drinking water. Other of hypothyroidism include a balding coat, excessive shedding, a substantially reduced heart rate, and lethargy. 3 In some cases, a dog will have thickened facial skin, sudden lameness (limping) or a loss of coordination, deposits of fat in the corneas, and an odd tilting of the head.