Dogwood trees that are established typically do not need fertilizer. If fertilizer is used on young trees, small portions of a slow-release fertilizer is ideal, according to Gardening Know How. Dogwood trees after becoming established do not need additional fertilization.
A dogwood tree is relatively easy to care for and needs a 6-inch watering once a week and a layer of mulch, according to Gardening Know How. Dogwoods should have dead limbs removed periodically but usually do not need pruning. If pruning is desired, do so in the summer so the trees do not bleed sap. Sap bleeds during the winter months if the trees are pruned at that time.