Is it true that the pulse can be felt on arteries but not on veins?

Yes, it's true. The beating of the heart only drives blood in the arteries. As the blood passes from the arteries to the capillaries and then to the veins, it ceases to be pumped by the heart, so no pulse can be felt. Blood in the veins returns to the heart because of the valves in the veins, and because of general muscular contractions in the body, rather than because of the heart.