Elastic compression stockings have no effect whatever on exercise, according to a study from France (European Journal of Applied Physiology, July 2006). They neither increase nor decrease endurance, strength, speed, recovery, or blood flow to the limbs. The study did not test the increased warmth generated by compression stockings, but many people with arthritis have difficulty exercising in the cold and feel better from the warmth generated by a snug wrapping. In hot weather, the support hose can act as a barrier to prevent heat loss, which may make you tire earlier.
Many people develop swollen feet and ankles when they stand or sit, which goes away when they lie down. People with this gravity-dependant swelling of their feet and legs often find that support stockings help to prevent fluid from collecting in their legs. While you exercise, the force of your contracting muscles keeps blood from pooling. When your leg muscles relax, the veins near them fill up with blood. When your leg muscles contract, they squeeze the veins near them and pump blood up toward your heart. The pumping action of your leg muscles exerts a strong force to empty your veins, so you will not need support hose during exercise. So you may benefit from wearing support hose when you stand around, but it is unlikely that you will need them when you exercise.