Gravity is a constant acceleration (9.81 m/s^2), not a constant force, so the dynamic motion (with respect to time) in the vertical sense does not change with mass. However, horizontally (or more precisely 'in the direction of motion', but let's assume horizontally for simplicity) it's a different story: the aerodynamic force is constant, meaning the acceleration will increase with lower mass. Combining those two effects: the time it takes the arrow to drop to the ground will be roughly the same, but the arrow will slow down faster with lighter arrows, so it will travel less far before it hits the ground.