I'm aware that headwind or tailwind does not affect rate of climb or descent but only the angle. I'm not sure if it affects the g force or not. I'd assume it affects g force because using trignometry, using SIN theta the vertical component increases as the angle increases. However a confirmation would be aappreciated.
In the takeoff run, the acceleration is less with headwind, but once in flight, the airplane flies within the mass of air. The fact that that mass may move in relation with the ground doesn't affect the magnitude of the forces involved in flight, so accelerations are not affected by the wind.
For flight at any given angle-of-attack, the aircraft's pitch attitude in space is tied to the climb or descent angle in relation to the airmass, not in relation to the ground.
The climb angle achieved with respect to the airmass does NOT change depending on whether the aircraft is facing upwind or downwind, and therefore the aircraft's pitch attitude in space doesn't depend on whether the aircraft is facing upwind or downwind.
Just as a glider's pitch attitude in space doesn't change as it circles with a given angle-of-attack and airspeed, even in the presence of a very strong tailwind that drops its groundspeed to zero at times.
So even if we recognize that the component of the G-load that acts in the "up and down" direction in the aircraft's reference frame is reduced when the aircraft is in a nose-high (or nose-low) pitch attitude, we won't see a difference in this value when we climb upwind versus downwind.
Note-- it is a bit ambiguous as to exactly what "G-load" means. Is it what we read on the G-meter-- i.e. just the component of "felt" acceleration that acts in the up-and-down direction in the aircraft's reference frame? If so, this is just equal to the component of the net aerodynamic force that acts in the up-and-down direction in the aircraft's reference frame. Essentially, the magnitude of the lift vector, divided by the aircraft weight. The steeper the climb angle, the smaller the lift vector -- see related answer Does lift equal weight in a climb? .
Or by G-load, do we mean the total "felt" acceleration, including the component that acts in the fore-and-aft direction in the aircraft's reference frame? If so, this is just equal to the net aerodynamic force the aircraft is generating, divided by the aircraft weight. Since in a stabilized climb with constant airspeed and constant direction of flight path, the net aerodynamic force generated by the aircraft IS exactly equal to weight, the G-loading by this definition would always be "1" in a stabilized climb, regardless of climb angle.
At any rate, by neither definition of "G-loading" do we see a difference when climbing upwind versus when climbing downwind. Nor do we see a difference in the aircraft's pitch attitude.
(Nuances-- this answer assumes that EITHER the pilot and G-meter are located at the aircraft CG in the fore-and-aft sense, or the pitch rotation rate is zero. Otherwise the relationship between G-meter reading (and "felt" acceleration) and aerodynamic force is influenced by the pitch rotation rate, as has been recently been pointed out in comments to other related answers. But even considering such added complications, no difference is caused by climbing upwind versus downwind.)
Key here is to realize that head wind, tail wind, climb, descent, Wright Flyer, sailplane, jet, balloon, the physics is the same regarding acceleration and non-accelerated flight. The four forces, simple as they seem, can be combined in an infinite number of orientations to achieve zero acceleration.
This is NOT necessarily just standing still, it can be an equilibrium of forces at a given velocity and direction. This, obviously but critically, applies to heavier than air flight. "If you ain't moving, you ain't flying". There for, in steady state flight, regardless of orientation or velocity, G force is only from gravity, and it is 1.
When you are only looking for the static acceleration that the pilot feels in his/her seat then the g-force is only a factor of the pitch attitude (theta). That is if we assume a stationary climb or descent, which by definition has a netto acceleration of zero. So 1g pulling the aircraft towards the ground, the more pitch attitude we have the more of the gravity has to be compensated by engine thrust to maintain an unaccelerated flight. This leaves less a smaller vertical g component. At 90deg pitch up the vertical component (from your pilot view) is going to be zero but the acceleration pushing you into the seat is now 1g (and engine thrust must equal aircraft weight). So in your fighter jet at 90 degrees nose up you will just feel as if you are lying on your back and you don't feel any vertical acceleration anymore, regardless of the wind speed.
- Ergo the vertical acceleration felt by the pilot in stationary flight is cos( theta ) * g, longitudinal acceleration on the pilot is sin( theta ) * g.