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I stop and walk across gravelly bits or iffy spots. Pebbles and bits in the trail can be a bit startling, but your foot will cup around them a little and your stride will adapt to get you off the pebble (less push-off with the toe if the pebble is under the ball of your foot, for example). Usually I can see what I'm running on. If I can't see it, it's probably under enough dirt that it's not likely to hurt me much.
I'm running on packed duff and dirt for the most part (under cedar and fir trees mostly) Have squished more than a few slugs between my toes. They pop. It's kind of icky. Some parts are reclaimed rail bed, those tend to be harder and have more gravelly personalities so I'm slower there.
Snow is just too cold for me to run far. Out the door, around the house, and back inside! I do like running on fresh snow, though. Briefly. 
Every year I have a full check with a dermatologist, and he's always surprised by the bottoms of my feet (which are quite lovely and healthy and hard). Like you, I was barefoot most of the time I was a kid. I also have a hard time finding shoes wide enough at the toes.
"If Americans want to live the American Dream, they should go to Denmark." - Richard Wilkinson