First of all you can always add a [`note`][1] on a way to add such information. The use of this tag by data consumers is limited, though. We have a series of keys that define attributes of physical accessibility that get recognized by renderers and routers (at least by those dedicated to hiking/cycling/...). The most suitable are:
[`surface`][2]
[`smoothness`][3]
[`sac_scale`][4]
[`mtb_scale`][5]
[`mtb_scale`][5]
[`trail_visibility`][6]
[`tracktype`][7] (for highway=track)
These are all somewhat subjective attributes but try to stick to the given examples and try to find a tagging that applies for most of the year and normal weather conditions. If has rained you can avoid paths with `surface=ground` but the way is not generally `smoothness=very_horrible` because of that.
If fallen trunks are left permanently you can consider that in your rating. If they just have not been removed yet after the last storm please leave them out. We don't maintain live data and some applications only update their databases every several months.
If there are actual physical permanent obstacles blocking the way you could also add one of the [barriers][8] to the path.
[1]: https://wiki.openstreetmap.org/wiki/Key:note
[2]: https://wiki.openstreetmap.org/wiki/Key:surface
[3]: https://wiki.openstreetmap.org/wiki/Key:smoothness
[4]: https://wiki.openstreetmap.org/wiki/Key:sac_scale
[5]: https://wiki.openstreetmap.org/wiki/Key:mtb:scale
[6]: https://wiki.openstreetmap.org/wiki/Key:trail_visibility
[7]: https://wiki.openstreetmap.org/wiki/Key:tracktype
[8]: https://wiki.openstreetmap.org/wiki/Key:barrier
