`smoothness=impassable` is popular and clear tag to mark that way is unpassable by any wheeled vehicle; see https://wiki.openstreetmap.org/wiki/Key:smoothness
There is also popular https://wiki.openstreetmap.org/wiki/Key:sac_scale to indicate how problematic it is for humans (and horses, I guess). In addition to previously mentioned tags, there is also some use of https://wiki.openstreetmap.org/wiki/Key:bicycle:physical to indicate physical possibility of using a bicycle (instead of legal restrictions), but it has some problems mentioned on their wiki, so I'd personally stick to the `smoothness=impassable` + `sac_scale=*`