Can a slow small plane, flying at a few meters above the ground, drop to the ground if the headwind abruptly stops?
Yes.  The theoretical concept of &quot;moving with the airmass&quot; essentially says that for any given constant wind or no wind, airspeed is dependent on thrust and drag and reaches a steady state.
However, in nature, especially close to the ground, obstacles such as buildings, trees and hills can make airflow anything but constant.
This is why the modern aviator adds a little airspeed when landing on windy days.  A gust or a lull can momentarily change your airspeed faster than the plane can restore its thrust/drag balance.
Wind shears are an extreme example of this.  Were it not for the wind, flying that Cessna would not be more difficult than driving a car.