Reading the original question I think the OP was really talking about steady state winds rather than changing ones, what you say here is true, but IMHO actually further complicating it, if you are going to go into this, you also need to add after
If the wind suddenly increases to 60 knots our lift will suddenly exceed our weight so we will rise. And our drag will suddenly exceed our that so we will move back wards over the ground. If the wind suddenly decreases the lift and drag will decreases, causing the aircraft to descend and move forward over the ground.
"if nothing is then done to change the power/attitude of the aircraft and with no further wind changes it will, after a short period of time, return to its original (air)speed and settle at its new altitude."