There is an unsurfaced road in a country park near me, with locked gates at either end. It’s available to the public as a footpath. It’s currently tagged as highway=unclassified, with 2 highway=gate nodes.
It shows on Mapnik as a through road, so I was going to add access=private, but that would suggest you can’t walk on it. Does the current tagging work (meaning it’s a rendering issue) or is there some other way to tag this correctly?