You can reboot a DAG witness server but only if your DAG cluster is operating with all of its members online.

An FSW (file share witness) will only come into play during a failover scenario. This means that it will become a problem if a DAG member fails at the exact same moment your FSW is rebooting, because the remaining DAG member will then not achieve majority, causing the cluster to fail completely.

Note that if you reboot the FWS often in a short period, the cluster will mark the FWS as unreliable and fail the cluster. In that case, you should manually bring it back online by running the following PS cmdlet on a DAG member:

Get-ClusterResource | Start-ClusterResource