ssh and remote sudo not hiding password

[Colin Law]

I can shut down a remote machine by connecting via ssh then shutting it down
ssh ip_address
<logon messages>
sudo shutdown -h now
password: (entered pwd not visible)

and the remote machine shuts down.
To save typing (and brain power) I wrote a script on local machine
ssh ip_addr sudo shutdown -h now
When I run the script it works as expected and shuts down the remote
machine, but when it prompts me for the password (for the sudo
shutdown), the password I type is not hidden but is visible on screen,
which is not good.  I am sure there is a way round this but I have not
managed to find it.  Any help will be much appreciated.

Colin