The fog might not be natural. The main forms of fog are: radiation fog; advection fog; and sea fog. Obviously Sea Fog could be discounted in this case - it's something I'm very used to from holidays in Whitby, where a fret can roll in off the sea within minutes, but they never spread to more than a mile or two inland.
Radiation fog is also very unlikely as this tends to form overnight when humid air meets a cool ground surface. These thick fogs might last throughout the day if the weather is still and cool enough (very common in the Yorkshire autumn) or they may also burn off to reveal a lovely sunny day (very common in Lancashire in the summer). The mist/fog which descends as they ride with Farmer Maggot may be a radiation fog as it forms lightly at dusk and the morning mist is described as lifting when they are in the Old Forest and find a gap in the trees
Advection fog is mostly unlikely as for this to form there would need to be either a large body of water (lake or sea) or a snow field. Of the sub types, frontal fog might be ruled out as the weather front has already passed over the day previously with Goldberry's Washing Day (and it sounds like it was a considerable front - was Middle-earth affected by the Jetstream?).
However, it could possibly be an Upslope fog, which forms when very humid and warm air is forced up a rising land mass by a steady and quite strong wind. However, there is no fog or mist described as hanging over the Old Forest earlier in the day when they set off across the Downs, the weather is very fine and bright.
What's described as falling on them that afternoon on the Downs is more like Scotch Mist, i.e. drizzle and low cloud. Not as evocative as fog, I'll give you, but if it's to have a meteorological answer, that'd be it, I reckon. I do
prefer the idea of some supernatural fog
