What is the red mist in Redbelly Mine in Skyrim?
Solution 1:
If you go deep enough into the mine, I'm pretty sure you will eventually see the red fog near the very bottom, but it has no impact on game play, so it's easy to miss. (As @Nelson points out below, the mist apparently doesn't appear unless you are using the Unofficial Skyrim Patch; for the special edition you can get that here, which includes the change:
The mine will also have modified visuals in an attempt to portray the described "red mist".
The best guess for what the red mist is, involves the nearby location of Redwater Den. This cave system is located near the western end of Redbelly Mine (there's a skooma lab in it). If you go deep enough into that cave system you'll eventually run into the Redwater Spring that gives all the nearby locations their name:
The most reasonable explanation is that the red mist is water vapon from the blood-red water, possibly coming from an underground waterfall, or evaporation, or whatever, that runs into the lower parts of the mine. As far as I know, the game never bothers to explain it specifically.
Solution 2:
You don't see the mist because the official version is not displaying it correctly.
This is fixed in the Unofficial Skyrim Patch 1.2.6.
Source