In an Exchange cluster with a Database Availability Group (DAG), you can easily "switch over" one, more or all mailbox databases to another node.

Warning
If you need to take a node offline, it's better to put it in maintenance mode. This will properly notify the cluster that the node is in maintenance and prevents automatic failover (of other services, if any) to other nodes.

Switchover can be done through EAC, or through the EMS (Powershell).

To switch over all mailbox databases to a server called EX2:

Move-ActiveMailboxDatabase -Server EX2

To switch over the database called DB1 to a server called EX2:

Move-ActiveMailboxDatabase DB1 -ActivateOnServer EX2

The switchover will  ...