The wooden trail has a fallen tree and the trail is pretty narrow. If you encounter someone, you will need to squeeze pass each other. There is a paved trail around the preserve that is bike friendly. I recommend staying on the paved trail.
The wooded section of trails are probably too narrow for bikes and pedestrians to safely share. But it also intersects with the Winchester Green Circle Trail, and there are paved sections that should be fine for biking. Check out: Check out: https://www.winchesterva.gov/green-circle-trail-sections
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