Thank you for your letter regarding fog. Apart from the usual inland fog that forms on clear cold nights there are several other types of fog, i.e. Frontal Fog, Hill Fog, Advection Fog + Coastal Fog. Strong to gale force winds are often associated with these types especially Frontal Fog + Hill Fog.
Remember fog is cloud. If you drive over high ground and we have a lot in this country then you can frequently drive into fog. Some roads are several thousand feet above sea level and are frequently in fog even with gale force winds.
Frontal Fog + Coastal Fog also arrive in the South West of England with strong to gale force winds. I can only assume your teacher taught you only about Radiation Fog, that's the sort I explained earlier:- cold, clear, little or no wind.