Hello welcome to OSM. The trails you removed in this changeset seems valid. If it exist on the ground should not be removed from OSM, regardless if its private or public, designated or informal.

These trails do seem to exist on the ground, They are visible from aerial imagery and show they are being used from heatmap data.

In OSM we don't remove features that exist. Please read for more info:
https://wiki.openstreetmap.org/wiki/Why_can%27t_I_delete_this_trail%3F

You also removed them in a way that left gaps in the trail that lead to "Peace Valley Overlook Trail". Please make sure you follow OSM editing best practices, and don't remove features that exist on the ground.

The correct way to handle this in OSM is to use the tagging system. access=no seems to apply here. Once this is done services that do use OSM data will reflect that and specify their access. 

I have restored the these trails, please use the tagging system if you think its appropriate, also please cite a reference or source. Thanks!