Well, this isn’t an easy one. Trails are really a mix. Dry dirt, wet dirt, thin layer of slush, snow.
All the above.
I’d say you could ride either. On a skinny there will be some awesome dirt sections offset by some sketchy spots. So if you want to err on the side of caution, bring your Fat Bike. You can’t go wrong. Want to have a mixed ride and are prepared for some “fun” (meaning sketchy) spots, bring your skinny.
There is no risk of trail damage by riding your skinny.
It is a beautiful day so get out and ride something, somewhere.