I definitely recommend this.
Running lights will make you more readily visible as the light will penetrate the fog to an extent.
Reflectors and high-viz clothing will be somewhat less effective during foggy conditions.
Use caution riding in foggy conditions as drivers may not see you until they are very close.
bicycles.stackexchange.com/users/2997/Benzo
You should use lights in fog.
On a car, you don't use high beams in fog (but you're supposed to use low beams (required) and fog lights (optional, but useful since they cast a low and wide beam which increases visibility) since they reflect back too much, but on a bicycle, your lights aren't that powerful for this to be a problem (and the distance they cover is less than a car light).
You should also be extra on edge and wear your high vis stuff, since your visibility is lower (and more importantly, people who are driving cars have lower visibility and aren't always very good at driving in fog).
bicycles.stackexchange.com/users/8219/Batman
Many people run lights on a clear day for safety.
In the US by law a motorcycle must run lights all the time.
Law was based on safety.
This is a related post
Does it make you safer to use lights during the day Cars turn their lights on in the fog.
Another answer was criticized for stating this is a no-brainier.
But it is.
As for high beam versus low beam.
A bicycle light is typically oriented as a low beam.
bicycles.stackexchange.com/users/7785/paparazzo
I always turn on my headlights even in the daytime for safety reasons, whether driving a car or riding a bike or motorcycle.
Many times I have tried to change lanes when visibility was limited and had to correct back into my lane because what I thought was a clear lane was actually occupied by a very hard to see vehicle coming up from my blind spot.
Many accidents could be avoided if everyone drove with their headlights on during limited visibility.
bicycles.stackexchange.com/users/13807/Rick Ryker
In Ohio, the way I read it, it appears that lighting falls under the generic vehicle lighting guidelines, so bicycles are required to act like cars in this one aspect (other rules explicitly state motorized vehicle or even "motorcycle").
So, lights are required when: Between sunset and sunrise Visibility less than 1000 feet Windshield wipers are on (recent addition which I think is reallydumb as we often have bright sunny days with occasional lightsprinkles and lights are totally unnecessary, yet you'll be using thewipers).
I've not yet seen a bicycle with wipers, so perhaps"raining enough that I'd use wipers if I had them
" would be a goodgeneral rule too?
bicycles.stackexchange.com/users/349/Brian Knoblauch
Today it was foggy, visibility was only slightly reduced, I already wear a high-vis on my bike but I am wondering if it is still worth me using my lights or is that overkill?
Should I use lights in foggy conditions?
bicycles.stackexchange.com
<safety><legal>
bicycles.stackexchange.com/questions/24735
bicycles.stackexchange.com/users/13790/Christopher Markwell
It is definitely recommended to switch your bike lights on when it is foggy. Reflectors and high visibility clothing are less noticeable in fog. Other vehicles are required to use lights in fog and, in the US, motorcycles must use lights at all times. According to law in the US: Lights are required:   Between sunset and sunrise  Visibility less than 1000 feet  Windshield wipers are on. Visibility is greatly reduced in fog and high visibility clothing is less effective, so lights are definitely recommended. Lights can improve visibility on a clear day, especially for motorcycles and bikes, and this is more important in fog. In some places, motorcycles must have lights on at all times for visibility, and other vehicles including bikes must use them in darkness, low visibility or rain.
Visibility is greatly reduced in fog and high visibility clothing is less effective, so lights are definitely recommended. Lights can improve visibility on a clear day, especially for motorcycles and bikes, and this is more important in fog. In some places, motorcycles must have lights on at all times for visibility, and other vehicles including bikes must use them in darkness, low visibility or rain.