Freestanding Fence Base Size
YES! You can build it exactly like the picture shows but with feet (on both sides) proportionally larger depending on final height and wind resistance required.

To ask what is wide enough "to keep it from falling over in the wind" is not answerable because it is too subjective; the right (wrong?) wind speed could take down almost anything. It would depend on materials used, method of construction, and wind load you would expect it to withstand. You could certainly build it with the knowledge that you do not know what conditions would tip it, and move it to a safe location whenever there is significant wind ("significant wind", again subjective). 

If you were to finalize the construction details (material, height, width, design details) a civil or structural engineer might be able to give you a ballpark wind shear resistance number.