bluskis,
I wondered myself, and after a very quick search found a (what seems to me reliable) source stating reported deaths of 1000s of migrating birds in fog.
http://www.darksky.ch/texte/sempach.pdf
(in German)
Birds do fly during fog. They are obviously being attracted by strong sources of light during fog, especially at night - collisions of flocks of birds with light houses etc. are common, according to that source.