The '03 springfields were made from around 1903 to 1944 (I think). There are several different versions of the same rifle: Rod bayonet, 1903, 1903 mk 1, 03A3, 03A4, and I'm probably missing one or two in between.
The only way you will be able to tell of the year it was made is by the serial number. Go to this site http://www.armscollectors.com/srs.htm find the right make of your rifle (remington, springfield, smith corona) and enter the serial number. It should give you a date of manufacture, or when it was used by a government agency last at least.