I would agree with most of your comments if you replaced "wind" with "gusts". How a plane aerodynamically responds to gusts is dictated by it's stability qualities. Don't confuse being blown around by a strong wind as being "unstable." There is a big difference. A plane with a cg too far aft is "unstable" regardless of winds. Gusts, on the other hand, would obviously have less effect on a heavier plane from an inertial standpoint.

Stability describes the aircraft's ability to return to its equilibrium state after experiencing a disturbance (usually from a gust, but not from a steady state wind). Static stability describes the aircraft's ability to INITIALLY return to it's original flight path. Dynamic stability describes the aircraft's ability to return to it's original flight path OVERTIME.

Stability is a trade off with maneuverability. "Powering into the wind" is simply that - power, or better "speed." It means simply flying faster than the headwind.

Also, don't always attribute the "twitchiness" of flying a plane into a strong headwind with a high power setting as being "unstable." You are probably experiencing a higher than normal airspeed in your attempt to maintain some type of groundspeed. And as a result, your controls are probably much more responsive and might feel "twitchier" than normal.

With all of this said, I love flying my sticks in the wind more than any of my other airplanes.