Ways that are still visible should not be removed.
Depending on the situation they may be tagged as abandoned (either with a prefix like "abandoned:highway=path" or simply "abandoned=yes) or one can add tags like
https://wiki.openstreetmap.org/wiki/Key:obstacle

Single trees across can be tagged as nodes with "barrier=*" as appropriate.

Please consult the wiki and the community before removing objects. There's always someone to help.

Cheers
Silversurfer83