The issue concerns much more than arrow mass is the reason. A better FOC may actually allow less drift for the lighter arrow due to weathervaning, although starting from zero velocity(the exact opposite if being launched from a bow), this would be much tougher to pull off in s short time, but gravity is a rocket engine given enough time. In addition, if the heavier arrow presented a much higher cross section for side drag, that force may overcome any inertial advantage.

Drag varies as the square with area, so much more force can be directed on a larger arrow pushing it further in the same amount of time. Because of the mass inertia, neither arrow will start drifting with the same velocity as the crosswind but will generally ramp up as time in the wind increases.