hedwards: It depends how short you're talking about. I found it to be hugely distracting when I played Turok, it seemed like the fog came in at about 10m and then you couldn't see anything at all. Same goes for some of the older race games.
I actually kinda liked the close fog in Turok (PC version), it gave a kind of eerie feeling to it, almost like Silent Hill (you never know what is coming out of the fog, even if you hear the sound already...).
In TES Arena the close fog is kinda distracting, but what can you do. I guess the graphics engine was already quite slow as it is when the game came out back in 1994 or so.
On the other side of the scale, I love how far you can see in Serious Sam games (at least the first two). Like in the starting place of the first game, you might get a glimpse of something glimmering faaaar in the desert, wondering if something really could be there. So you start going towards it, and after a few big fights and stuff, yep, there is an oasis with some goodies.
I think those Serious Sam games showed you don¨t need a slow and demanding graphics engine in order to see for miles.