Apparently, Outlook 2003 uses IE to print HTML messages (and I assume
it probable handles plain-text, too, but don't know for sure).
If you open Internet Explorer, and open the File Menu, you will see a
"Page Setup..." option, just above "Print..."
Open that up, and you will see settings for Headers and Footers. The
defaults in my IE7 are:
&w&bPage &p of &P (Header)
&u&b&d (Footer)
Perhaps if you clear these, or at least the footer, accept the
settings, and then try to print a message from Outlook, it will print
without the date.
If you want to restore the defaults afterward for regular printing
from IE, copy mine from this post or save a .txt file with those
strings locally.
Let us know if this works; as I don't have an installation of 2003 on
which to test it.