That depends on the law of the country. We have access tags to map that. Haven’t you said to the same a few times already 
It is tagged bicycle=no because of the country it is in and some signs on the way to get there. Nobody ever bothered to tag horse=no. I now did invite Nop to share opinion.
It is mapped as path. It is wide enough for a car, but does that matter? Predominant use is walking. I would find it confusing though, if such a thing would be a trail in Austria and a path in Germany just due to legal matters. In yet other parts of the world it might be mapped as footway.