Hi,

This is not the correct way to show that it is closed, most routers will ignore noexit tags. You need to use either access=no or highway=construction (if it's being worked on) on the part of the trail that's closed, using https://wiki.openstreetmap.org/w/index.php?title=Conditional_restrictions&uselang=en if it's only closed for a short period of time.

If there are physical barriers, then you can also map them as https://wiki.openstreetmap.org/wiki/Key:barrier.

Hope this helps!