Is there an easy way to have sshd send a shutdown alert at login, if a shutdown is currently planned? The alert works fine if people are already logged in, but it does not alert those who login after the command is sent.

Similarly, is there an easy way to send periodic reminders? Maybe just write a script?

Thanks in advance!

Sending messages is not something ssh can do. There are three options
you might want to consider.

The /etc/motd file is printed when a user logs in. That would be the
place to put any messages that you want people to see.

If you just want to send a message to all users that are already logged
in, use wall.

If you want to manage the whole process, read the man page for shutdown.
You can schedule the shutdown to happen in the future, prevent new logins,
and send a message to users with one command. You can also use the -k
option to send a message without really scheduling the shutdown.

pam_nologin is what you want: http://linux.die.net/man/8/pam_nologin