The rendering cost of Exponential Height Fog is similar to two layers of constant density height fog with an additional optimization:
The !FogStartDistance can be used to artificially keep some defined area in front of the viewer without fog. This also helps performance as pixels can be culled by the z buffer.
The following images show this applied:
Fog Start Distance = 0
Fog Start Distance = 1000
Fog Start Distance = 1000 with a high Fog Density value
Depending on the scene content and when using a far fog start distance, the rendering cost can be 50% or less.
This optimization is implemented by rendering a full screen quad that has a z value and depth test enabled.