The veins just below the skin in the arms and legs are unsupported by adjacent muscle tissue and are more prone to expansion due to pressure. The greatest influence is gravity. This is most evident by its cause for varicose veins....the valves in the legs are there to keep the blood from pooling due to gravity, however over time they begin to leak and the resulting pooling of blood results in greatly expanded veins. This effect is less prominent in the arms for a variety of reasons...closer to heart and horizontal mobility. One of the reasons some folks wear support stockings/ sit with legs raised.
The bulging vessels in my hands are veins. Some veins, such as those in the legs, have special flaps which trap blood to prevent it flowing back down to your feet through gravity. This is why surgeons have to ensure they are the right way around when grafting as a bypass, or they sometimes destroy the flaps.
Your system of arteries taking the blood to the hands is not having to fight gravity when your hands are down, whereas it does have to fight against gravity when your hands are up. So, when your hands are down, the blood easily flows downward through your arteries into your arterioles and capillaries and then starts the return to your heart through your veins to be reoxygenated via the lungs, then pumped back out of your heart to your arterial system once again.
Also, in the summer, your blood vessels tend to dialate because of the heat (the same would be true if you soaked your hands in hot water)- the heat makes the vessels relax, accounting for the additional bulging when compared to the colder weather of winter, where your blood vessels would tend to be more constricted.