Visual indications are so great, aren't they? I do it with terminals, too; prod servers get obnoxious red-background prompts. (Root terms on all my machines look different from unprivileged ones, too.)
echo '\033]11;#440000\007'
On the local machine add this to reset the terminal color: ssh () {/usr/bin/ssh "$@"; echo '\033]11;#000000\007'}