My fingers swell when I exercise, even when I take a long walk on warm days. What might be causing this?

Puffy Palms. Exercising and warm days have one thing in common which can cause this. Both increase your body temperature. The way your body then regulates its temperature to keep you "even" is to dilate blood vessels and perspire. This may explain why your hands swell. Gravity also contributes to this, pulling fluid down into the hands and feet on warm days and explains why veins also "bulge" on warm days.
Probably normal. I doubt anyone has ever studied this completely, but I believe it is a normal response to exercise in many people as I too experience it. I'm quite sure it has to do with the redistribution of blood in the body during exercise through the physiological process of the blood vessels dilating. Limit your daily sodium intake to 2 grams; sodium may aggravate it and may also cause high blood pressure.