The FAAs Pilots Handbook of Aeronautical Knowledge defines it as: "Best angle-of-climb speed (VX)—the airspeed at which an aircraft gains the greatest amount of
altitude in a
given distance. It is used during a short-field takeoff to clear an obstacle." --Distance is measured on the ground, hence why I consider it a ground reference and why wind matters.
Below is a typical chart, where Vx is shown in zero wind. To find Vx, you divide the "rate of climb" by "ground speed" and find the maximum. For basic pilot training, zero wind is assumed, so ground speed and airspeed are identical. Flight manuals are also based on zero wind conditions, and aircraft have instruments that measure air speed. --Flight manuals are done this way because it is simple, and because flying Vx with with a headwind will give a better angle of climb for obstacle clearance. i.e. the flight manuals are conservative and you will see a better angle of climb with a headwind than the published numbers.
The problem comes when you want to
measure/observe Vx with a headwind. The best angle actually happens at a slightly slower airspeed (slightly because the graph is steep in that region). Think of an extreme example. Assume your gyro can climb at 1 foot per minute at 40 MPH. With a 40 MPH headwind, flying at 40 MPH would give you a vertical climb, which is the absolute "Best Angle of Climb". It would take you all day long to get to altitude, but it would be the best angle you observed.
View attachment 1146600
Now, what should a pilot fly. The basic pilot should look in their flight manual and see what what distance they need to clear an object when flying Vx. If they can make it, they should fly Vx. A headwind only makes the angle of climb steeper. Its why manuals specify Vx with zero wind conditions. And it is also why tailwind takeoffs are bad for obstacle clearance. (Down hill vs tail wind is always a fun discussion)