Fog isn't really a "thing". It's a lighting effect so it's pretty much cast where the camera is looking.
You could fake a ground fog with textured ghosted planes overlapping each other and slowly scrolling the textures.
Use arrow keys to move and mouse to steer
set display mode 800,600,32
sync on
sync rate 60
autocam off
hide mouse
randomize timer()
rem make a smokey texture?
for n=1 to 10000
c=rnd(255)
ink rgb(c,c,c),0
x=rnd(256)
y=rnd(256)
dot x,y
next n
for n=1 to 6
blur bitmap 0,2
next n
get image 1,0,0,256,256
sync
make matrix 1,1000,1000,25,25
for obj=1 to 10
make object plain obj,1000,1000
texture object obj,1
ghost object on obj
position object obj,500,rnd(12),500
zrotate object obj,rnd(360)
xrotate object obj,90
next obj
obj=0
do
for obj=1 to 10
scroll object texture obj,.0003,0
next obj
gosub _move_camera
sync
loop
`----------------------------------------------------------------
_move_camera:
move camera (upkey()-downkey())*5
yang#=wrapvalue(camera angle y()+mousemovex())
yrotate camera yang#
return
`----------------------------------------------------------------
Enjoy your day.