I made some dense smoke in cycles with the Quick Smoke simulation. I want the smoke to be blown to the left of the scene as if it's coming out of a smokestack, so I added a wind force field. No effect. I turned up the strength, still no effect. I even added another wind force field, yet the smoke still stubbornly rises straight up.
The force field in the scene is being affected by a high dampening due to the simulation of gravity introduced by the Falloff settings you are using. The wind is now acting as if it was dragged down by a strong force that is currently erasing its influence on the smoke.
If it is suitable for your project, my suggestion would be to simply come back to the default value of Falloff Power = 0.