It would require general understanding of the BMP format and being able to build a file via a script or a program. Since this is a custom format used only by the game, you would need to create your own converter for this. Another thing to keep in mind is, you need to obtain the palette, as well as the width and height of the bitmap used in the .fex files separately, since they are not stored all together unlike normal BMP. As already said, these .fex files are raw data only.
The simplest way to edit them without any special tools would be via a hex editor. One byte = 1 pixel, where the value represents the index in the palette. However, it is a very uncomfortable representation, and you simply wouldn't easily know the location of each pixel on the bitmap (especially with the width/height parameters unknown).