Juster mentioned the Tyndall effect. I never heard of it before so I looked it up
in Wikipedia and found it to refer to the scattering of light by a suspension of particles (which fog would count as). The Tyndall Effect explains why you can "see" a beam of light passing through fog, or why light scattered by a suspension tends to be bluer than the light that passes through. But it does not suggest that light beams will *bend* when passing though a fog. I don't think it explains why fog would shift your wind zero.
Let's go over Jerry's list.
Having shot in the same location before on a different day (presumably from the same spot, to the same target?), with the same rifle and the same load does eliminate a lot of possible explanations. For example, even if your scope was not tracking straight up and down, this wouldn't matter because your scope on day#1 would be set to exactly the same setting (I presume) as when you fired on day#2. Similarly, we can eliminate spin drift (it would be the same each day).
It could be cant (some or all of it). If you canted your rifle 5 degrees or 6 degrees differently on one day vs. the other, this would explain a 1.5 MOA sideways shift in your POI at 600 yards (I've assumed a typical .308/168@2600fps, dropping about 16 MOA at 600 yards).
It could be an error in what you think your wind zero is. Chances are that the actual wind on your foggy day was as close to truely zero as you've ever been able to shoot in. But maybe your recorded wind zero from a clear day could be out by 1/2 MOA or even 3/4MOA?