I think smoothness is that tag 
I would tag such paths with incline=* (and let the map user decide if that is too steep for them), barrier=log, obstacle=fallen_tree or obstacle=vegetation It is more informative than just mapping that a path is impassable, and gives the map user more freedom to decide whether to use that path or not, depending on skills, desire, need to use, etc. An MTB rider might decide that he’ll climb over the fallen trees carrying his bicycle and then continue cycling.