I'm wondering if I would get any extra miles on a long trip if I made sure the headlights and fog lights were both off during the day. I know LED lights don't use a lot of power, but I'm still curious if I might get a few extra miles by keeping the lights off during the day on a long trip.
Agreed with all of the above; don't worry about it. The impact will depend on your average speed, of course (if you travel faster you don't have to have them on as long, so you'll consume less energy per mile).
To put some numbers to it, a quick Google search for LED headlights indicates 15-45 watts consumption. I'll pick 30W. Seems reasonable when considering how bright a 15W standard issue house LED lamp is. These lights are a few thousand lumens (probably 3000-4000?), and 100 lumens per watt seems about right for "good" LED efficiency.
So, 60W for two headlights. The fog lights are going to be lower of course, I'd guess maybe 20W total.
So 80W total.
20mph avg speed: 80W/20mph = 4Wh/mi
40mph avg speed: 80W/40mph = 2Wh/mi
60mph avg speed: 80/60mph = 1.33Wh/mi
So not a huge impact!