VM
The correct way of coding is that if it is below 0 degrees, and less than 1000m,then it is FZFG. This is simpler for (relatively) untrained Met Observers to cope with and gives element of objective standardisation, rather than the subjective 'are the water dorplets super-cooled or not?'
Having said that, if you examine a lot of METARS in such conditions, many reporters still forget to call it FZFG when it is less than 0 degrees; I would suggest that if it is reported as FG (only) with the temp below 0, that you treat it as freezing fog, for an aircraft operation point of view.