I am still confused whether a head wind or tailwind would affect the rate of climb. Since in a HW/TW condition our a/c is basically still climbing in the same parcel of air, it is just that parcel of air is moving with or against our course hence increasing/decreasing the horizontal distance covered to get to the target height. This means that the time needed to get to the target altitude is not affected at all, but the horizontal distance is.
Yet my friends have been insisting that with a headwind an aircraft would climb faster to the target height, as the headwind helps create more lift by increasing the amount of air passing through the wings.